A woman stands at the edge of a cliff and throws a pebble horizontally over the edge with a speed of v0 = 20.5 m/s. The pebble leaves her hand at a height of h = 55.0 m
above level ground at the bottom of the cliff, as shown in the figure. Note the coordinate system in the figure, where the origin is at the bottom of the cliff, directly below where the pebble leaves the hand. Answer parts a-f.

Answer:

3.79 m/s^2

Explanation:

We know the small part loses 0.932 MJ of gravitational potential energy during its fall.

Potential energy = mass x gravitational field strength x height

Re-arranging to solve for gravitational field strength:

g = Potential energy/(mass x height)

Plugging in the given values:

g = 0.932 MJ / (1.8kg x 140km)

= 0.932 x 10^6 J / (1.8 x 1000kg x 140 x 1000m)

= 3.79 m/s^2

Therefore, the gravitational field strength of Mars is calculated to be 3.79 m/s^2.

Answer:

D.  1.4 m/s

Explanation:

forward direction is +

back direction is -

Momentum = P = mass x velocity = mv

let v =  velocity of ball after collision

Law of Conservation of Momentum:  total momentum before the collision must equal the total momentum after the collision

(0.20 kg)(5 m/s) + (1 kg)(0 m/s) = (0.2 kg)(-2 m/s) + (1 kg)v

1 kg·m/s + 0 = -0.4 kg·m/s + (1 kg)v    

1 kg·m/s + 0.4 kg·m/s =  (1 kg)v    rearrange the equation and solve for v

(1 kg)v  = 1.4 kg·m/s

v = (1.4 kg·m/s) / (1 kg) = 1.4 m/s

Explanation:

acceleration definition = change in velocity / change in time =

(630 - 581)  m/s  /  5 s = 49 / 5 = 9.8 m/s^2  was the deceleration

Answer: the material involved in the change is structurally the same before and after the change. Types of some physical changes are texture, shape, temperature, and a change in the state of matter. A change in the texture of a substance is a change in the way it feels

Explanation:

Suppose that you're facing a straight current-carrying conductor, and the current is flowing toward you. The lines of magnetic force at any point in the magnetic field will act in option c)  the direction opposite to the current.

Lenz's law is the law that governs the direction of magnetic force.According to Lenz's law, magnetic fields induced by an electric current have a polarity such that the current's magnetic field opposes any change in current flow. Based on this law, the induced current must produce a magnetic field that opposes the current that produced it.

If the current is flowing towards us, the induced magnetic field must flow in the opposite direction to the current. Therefore, the direction of the lines of magnetic force at any point in the magnetic field will act in the direction opposite to the current.Hence, the correct option is C) the direction opposite to the current.

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Option A. The angle between the force and displacement is 180°, the maximum work is considered to be done by the force.

Work is defined as the product of the force applied to an object and the displacement of the object in the direction of the force. Mathematically, work (W) is given by the equation:

W = F * d * cos(theta)

Where

F = magnitude of the force

d = magnitude of the displacement

theta = angle between the force and displacement vectors.

In order to maximize the work done by a force, we need to maximize the value of the cosine of the angle theta. The cosine function reaches its maximum value of 1 when the angle theta is 0° or 180°.

When the angle between the force and displacement is 0° (option E), the force and displacement vectors are perfectly aligned in the same direction. In this case, the work done is maximized. Therefore, the correct answer is option A.

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Guiseppe's buys supplies to make pizzas at a cost of $4.02. Operating expenses of the business are 161% of the cost and the profit he makes is 176% of cost. The regular selling price of each pizza is $7.33.

Let's denote the cost of supplies as C.

Operating expenses:

The operating expenses of the business are 161% of the cost. Therefore, the operating expenses can be calculated as:

Operating Expenses = 1.61 * C

Profit:

The profit made by Guiseppe is 176% of the cost. Therefore, the profit can be calculated as:

Profit = 1.76 * C

Total cost:

The total cost includes the cost of supplies and the operating expenses:

Total Cost = C + Operating Expenses = C + 1.61 * C = 2.61 * C

Regular selling price:

The regular selling price is the sum of the total cost and the profit:

Regular Selling Price = Total Cost + Profit = 2.61 * C + 1.76 * C = 4.37 * C

Given that the cost of supplies is $4.02, we can substitute this value into the equation:

Regular Selling Price = 4.37 * 4.02 = $17.5674

Rounding the final answer to the nearest cent, the regular selling price of each pizza is approximately $7.33.

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The cardinality of R₁ \ (R₁ intersection A) is 4. The given polynomial (2x² + y² + 22 - 8x + 2y - 2xy + 2xz-16z + 35) cannot be solved for x, y, and z due to insufficient equations.

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(a) The amplitude of the wave is 0.2 m.

(b) The period of the wave is  4 s.

(c) The wavelength of the wave is 100 m.

(a) The amplitude of the wave is the maximum displacement of the wave.

amplitude of the wave = 0.2 m

(b) The period of the wave is the time taken for the wave to make one complete cycle.

period of the wave = 5.5 s - 1.5 s = 4 s

(c) The wavelength of the wave is calculated as follows;

λ = v / f

where;

f = 1/t = 1 / 4s = 0.25 Hz

λ = ( 25 m/s ) / 0.25 Hz

λ = 100 m

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Answer:

C) Carpet

Explanation:

If you were trying to build a soundproof room, the material that would absorb the most sound would be carpet. Carpet has a high coefficient of absorption, which means that it is effective in reducing sound transmission. Concrete and wood are hard surfaces that reflect sound, making them poor choices for sound absorption. Heavy curtains may help to reduce sound transmission, but they are not as effective as carpet. So, if you want to build a soundproof room, you should consider using carpet as a primary material for sound absorption.

Answer:

5 m/s

Explanation:

We are given that 9000 kg of water flows through the pipe in 1 minute. Mass flow rate = mass/time

So, mass flow rate = 9000 kg / 1 minute = 150 kg/s

We know the cross sectional area of the pipe is 0.3 m2. From continuity equation, mass flow rate = density * area * velocity

So, 150 = 1000 * 0.3 * v (Density of water is approximately 1000 kg/m3)

Solving for v (velocity):

v = 150/(1000*0.3) = 5 m/s

Therefore, the speed of water in the pipe is 5 m/s.

a. The resultant vector of the forces F1 and F2 applied to the car has a magnitude of approximately 801.86 N and is directed approximately 19.85 degrees to the right (forward direction).

b. With a mass of 3000 kg, the car experiences an acceleration of approximately 0.2673 m/s² when subjected to the given forces, neglecting friction.

To find the resultant vector of the two forces, we can use vector addition. The given forces are F1 = 445 N and F2 = 368 N. Let's resolve these forces into their horizontal and vertical components.

For F1:

The angle between the normal and F1 is 10 degrees. We can find the horizontal and vertical components using trigonometry.

Horizontal component of F1 = F1 * cos(10 degrees)

                          = 445 N * cos(10 degrees)

                          ≈ 438.37 N

Vertical component of F1 = F1 * sin(10 degrees)

                        = 445 N * sin(10 degrees)

                        ≈ 77.06 N

For F2:

The angle between the normal and F2 is 30 degrees. Again, we can use trigonometry to find the components.

Horizontal component of F2 = F2 * cos(30 degrees)

                          = 368 N * cos(30 degrees)

                          ≈ 318.64 N

Vertical component of F2 = F2 * sin(30 degrees)

                        = 368 N * sin(30 degrees)

                        ≈ 184 N

Now, we can add the horizontal and vertical components separately to find the resultant vector.

Horizontal component of the resultant vector = Horizontal component of F1 + Horizontal component of F2

                                           ≈ 438.37 N + 318.64 N

                                           ≈ 757.01 N

Vertical component of the resultant vector = Vertical component of F1 + Vertical component of F2

                                         ≈ 77.06 N + 184 N

                                         ≈ 261.06 N

To find the magnitude of the resultant vector, we can use the Pythagorean theorem:

Magnitude of the resultant vector = sqrt((Horizontal component)^2 + (Vertical component)^2)

                                = [tex]\sqrt{((757.01 N)^2 + (261.06 N)^2)}[/tex]

                                ≈ 801.86 N

The direction of the resultant vector can be found using trigonometry:

Direction = arctan(Vertical component / Horizontal component)

         = arctan(261.06 N / 757.01 N)

         ≈ 19.85 degrees to the right (forward direction)

So, the resultant vector of the two forces has a magnitude of approximately 801.86 N and a direction of approximately 19.85 degrees to the right (forward direction).

Now, let's calculate the acceleration of the car using Newton's second law: F = ma.

Given that the mass of the car is 3000 kg, we can rearrange the equation to solve for acceleration:

Acceleration = Force / Mass

Using the magnitude of the resultant vector (801.86 N), we have:

Acceleration = 801.86 N / 3000 kg

            ≈ 0.2673 m/s²

Therefore, the car has an acceleration of approximately 0.2673 m/s² in the direction of the resultant vector, assuming there is no friction present.

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The graphic organizer suggests that the job of an astronaut is complex, demanding, and involves flight.

This conclusion can be drawn by examining the nature of the requirements listed in the graphic organizer. Firstly, the requirements listed in the organizer are numerous and encompass various aspects. They include educational qualifications, such as having a bachelor's degree in a relevant field, as well as specific experience, like piloting an aircraft.

These requirements highlight the complexity of the job and indicate that astronauts need to possess a diverse set of skills and knowledge. Additionally, the requirements for physical fitness and health demonstrate the demanding nature of the job.

Astronauts are expected to undergo rigorous physical training to ensure they can handle the physical stresses associated with space travel and the conditions they will encounter in space. This indicates that the job can be physically exhausting and requires individuals to be in excellent health.

Lastly, the inclusion of flight-related requirements, such as the need to pass a long-duration spaceflight physical and participate in aircraft flights, implies that the job of an astronaut involves actual flight experiences. This indicates that astronauts are directly involved in piloting spacecraft and are expected to have practical experience in flying.

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If two waves with equal amplitudes and wavelengths travel through a medium in such a way that a particular particle of the medium is at the crest of one wave and at the trough of the other wave at the same time then D) The particle will remain stationary due to interference.

When two waves with equal amplitudes and wavelengths pass through a medium, they undergo interference. Interference occurs when the crests and troughs of the waves overlap. In this case, if a particular particle of the medium is at the crest of one wave and at the trough of the other wave at the same time, it experiences what is called destructive interference.

Destructive interference happens when the peaks (crests) of one wave align with the troughs of the other wave. In this situation, the positive displacements caused by the crest are canceled out by the negative displacements caused by the trough. As a result, the net displacement of the particle is zero, and it remains stationary.

This phenomenon occurs due to the principle of superposition, which states that the total displacement of a particle at any point in a medium is the vector sum of the individual displacements caused by each wave. Therefore, in this scenario, the particle will remain stationary due to the destructive interference between the two waves. Therefore, Option D is correct.

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Answer: D

Explanation:

In this case, the demand (D1) moves to the left (D2), this also happens with supply (S1) leading to (S2), moreover, the intersections between these lines represent E1, E2, and E3.

Due to an increase in salary, it is expected the demand for dinners increase, which means this line would move to the left. This occurs as a higher wage for everyone implies people are more willing to pay for dinner than before.

This change would also mean restaurants are likely to provide more quantity, which increases the supply, and therefore in this process the equilibrium changes.

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Answer:

1. Concave mirror

2. Convex mirror

3. Concave mirror

4. Concave mirror

Explanation:

Concave mirror is placed near on an object it displays a virtual image

Answer:

[tex]\displaystyle \frac{M + m}{m}\, \sqrt{2\, x\, u\,g}[/tex].

Explanation:

This question can be solved in the following steps:

Assume that the table is level. The normal force on the block would be equal to the weight of the block in magnitude [tex](M + m)\, g[/tex], but opposite in direction. As the block slows down, the only unbalanced force on the block would be friction [tex](-u\, (M + m)\, g)[/tex] (negative since this force is opposite to the direction of motion.)

The acceleration of the block would be:

[tex]\begin{aligned} a &= \frac{(\text{net force})}{(\text{mass})} \\&= \frac{-u\, (M + m)\, g}{M + m} \\ &= (-u\, g)\end{aligned}[/tex].

Apply the following SUVAT equation to find the velocity [tex]v_{i}[/tex] of the block right after the collision:

[tex]\displaystyle {v_{2}}^{2} - {v_{1}}^{2} = 2\, a\, x[/tex],

Where:

Rearrange and solve for [tex]v_{1}[/tex], the velocity right after collision:

[tex]\begin{aligned}v_{1} &= \sqrt{{v_{2}}^{2} - 2\, a\, x} \\ &= \sqrt{0^{2} - 2\, (-u\, g)\, x} \\ &= \sqrt{2\, x\, u\, g}\end{aligned}[/tex].

Apply the conservation of momentum to find the velocity of the bullet before the collision. Right after the collision, sum of momentum would be:

[tex](M + m)\, \sqrt{2\, x\, u\, g}[/tex].

Right before the collision, sum of momentum would be:

[tex]m\, v_{0}[/tex].

By the conservation of momentum:

[tex]m\, v_{0} = (M + m)\, \sqrt{2\, x\, u\, g}[/tex].

Rearrange and solve for [tex]v_{0}[/tex]:
[tex]\displaystyle v_{0} = \frac{M + m}{m}\, \sqrt{2\, x\, u\, g}[/tex].

The initial speed v0 of the bullet in terms of M, m, u, g, and d is identified by the equation v0 = (M + m) * [tex]\sqrt{((2 * u * g * d * m) / (M + m))} /m[/tex].

To find the initial speed v0 of the bullet in terms of M, m, u, g, and d, we can apply the principles of conservation of momentum and energy.

First, let's consider the conservation of momentum. Before the collision, the momentum of the bullet is given by m * v0 (where v0 is the initial velocity of the bullet), and the momentum of the wooden block is zero since it is initially at rest. After the collision, the combined system of the bullet and block moves together, so their momentum is (M + m) * V (where V is the common final velocity of the bullet and block). Since momentum is conserved, we have:

m * v0 = (M + m) * V

Next, let's consider energy conservation. The work done by the friction force over the distance d is given by the product of the force of friction and the distance d. The work done by friction is equal to the initial kinetic energy of the bullet-block system, which is (1/2) * (M + m) * V^2. Thus, we have:

(1/2) * (M + m) * V² = u * (M + m) * g * d

Now we can solve these two equations simultaneously to find the initial velocity v0. Rearranging the first equation, we have:

v0 = (M + m) * V / m

Substituting this expression for v0 into the second equation, we get:

(1/2) * (M + m) * [(M + m) * V / m]² = u * (M + m) * g * d

Simplifying and solving for V, we obtain:

V = [tex]\sqrt{((2 * u * g * d * m) / (M + m))}[/tex]

Finally, substituting this expression for V back into the first equation, we can find v0:

v0 = (M + m) * [tex]\sqrt{(2 * u * g * d * m) / (M + m)}[/tex] / m

Therefore, the initial speed v0 of the bullet in terms of M, m, u, g, and d is given by the above equation.

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When white light reflects off of a green surface, only the green wavelengths of light are reflected (option d).

1. White light is a combination of all visible wavelengths of light, including red, orange, yellow, green, blue, indigo, and violet.

2. When white light hits a green surface, the surface absorbs some wavelengths of light and reflects others.

3. The color we perceive as "green" is the result of the green wavelengths of light being reflected by the surface.

4. In this case, the green surface absorbs all the wavelengths of light except for the green wavelengths, which are reflected back.

5. As a result, our eyes detect the reflected green light and interpret it as the color green.

6. This phenomenon occurs because the green surface selectively absorbs and reflects different wavelengths of light based on its molecular structure and the interactions between light and matter.

7. The absorption and reflection of specific wavelengths of light give objects their perceived color.

8. Therefore, when white light reflects off of a green surface, only the green wavelengths of light are reflected, while the other wavelengths are absorbed by the surface.

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Answer:

To solve this problem, we need to use some principles of physics, specifically Newton's second law (F=ma) and the equations of motion. Here are the steps:

1. Calculate the acceleration (a)

We can use the equation of motion to find the acceleration:

v_f^2 = v_i^2 + 2a*d

where:

v_f = final velocity = 6.80 m/s

v_i = initial velocity = 3.00 m/s

d = distance = 2/3 of the length of the fish = 2/3 * 1.50 m = 1.00 m

a = acceleration (which we are trying to find)

Rearranging the equation to solve for a gives us:

a = (v_f^2 - v_i^2) / (2*d)

2. Calculate the magnitude of the force F

Once we have the acceleration, we can use Newton's second law (F=ma) to calculate the force. The net force acting on the fish as it jumps out of the water is the difference between the upward force F exerted by the tail fin and the downward force due to gravity (mg). The net force is also equal to the product of the mass of the fish and its acceleration (ma). Therefore, we have:

F - mg = ma

Rearranging this equation to solve for F gives us:

F = ma + mg

Now let's plug in the numbers and do the calculations.

First, let's find the acceleration:

a = (v_f^2 - v_i^2) / (2*d)

a = (6.80 m/s)^2 - (3.00 m/s)^2) / (2*1.00 m)

a = (46.24 m^2/s^2 - 9.00 m^2/s^2) / 2 m

a = 37.24 m^2/s^2 / 2 m

a = 18.62 m/s^2

The salmon's acceleration is 18.62 m/s^2 upward.

Next, let's find the force F. We know the mass of the fish is 52.0 kg, and the acceleration due to gravity is approximately 9.8 m/s^2. So,

F = ma + mg

F = (52.0 kg)(18.62 m/s^2) + (52.0 kg)(9.8 m/s^2)

F = 969.24 N + 509.6 N

F = 1478.84 N

So, the magnitude of the force F exerted by the salmon's tail fin during this interval is approximately 1479 N.

a.  the tension in the rope is  91.5 N.

b.   the moment of inertia of the wheel is  0.1008 kg⋅m².

c.  the angular speed of the wheel 2.30 s after it begins rotating is  38.34 rad/s.

(a)

The tension in the rope can be found by considering the forces acting on the object.

ma = mg*sin(θ) - T

(14.0 kg)(2.00 m/s²)

= (14.0 kg)(9.8 m/s²)*sin(37°) - T

T = (14.0 kg)(9.8 m/s²)*sin(37°) - (14.0 kg)(2.00 m/s²)

T =  91.5 N

(b)

The moment of inertia of a wheel:

I = (1/2)MR²

I = (1/2)(14.0 kg)(0.12 m)²

I = 0.1008 kg⋅m²

(c)

The angular acceleration of the wheel:

α = a/R

α = angular acceleration,

a = linear acceleration of the object,

R =  radius of the wheel.

α = (2.00 m/s²)/(0.12 m)

α = 16.67 rad/s²

The angular speed (ω) of the wheel after time t is :

ω = ω₀ + αt

ω = 0 + (16.67 rad/s²)(2.30 s)

ω = 38.34 rad/s

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For a bomber flying horizontally over level terrain:

(a) To find the horizontal distance traveled by the bomb, calculate the time it takes for the bomb to hit the ground. Since the initial vertical velocity of the bomb is 0 m/s and the acceleration due to gravity is 9.8 m/s², use the equation:

Δy = v₀yt + (1/2)at²

where Δy = change in vertical position (altitude), v₀y = initial vertical velocity, t = time, and a = acceleration due to gravity.

Plugging in the values:

Δy = -2.50 km = -2500 m (negative because it's downward)

v₀y = 0 m/s

a = -9.8 m/s²

Rearrange the equation to solve for t:

t = √(2Δy/a)

t = √(2(-2500 m)/(-9.8 m/s²))

t ≈ 16.07 s

Since the horizontal velocity of the bomb is 290 m/s, calculate the horizontal distance traveled:

Δx = v₀xt = (290 m/s)(16.07 s)

Δx ≈ 4657.3 m = 4.6573 km

Therefore, the bomb travels approximately 4.6573 km horizontally between its release and its impact on the ground.

(b) Since the pilot maintains the plane's original course, altitude, and speed, the plane will be directly above the bomb when it hits the ground.

Answer: directly above the bomb

(c) Since the bomb hits the target seen in the sight at the moment of release, the bombsight must be set at an angle equal to the angle of depression from the horizontal.

Using trigonometry, find this angle:

tan θ = Δy / Δx

θ = tan⁻¹(Δy / Δx)

θ = tan⁻¹(-2500 m / 4657.3 m)

θ ≈ -29.11°

Since the angle is measured forward from the vertical, the bombsight is set at approximately 29.11° forward from the vertical.

Therefore, the bombsight is set at an angle of approximately 29.11° forward from the vertical.

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The function of the power supply is to provide electrical energy to the device or system that needs it. The power supply converts the incoming voltage from the power source into a form that is usable by the device, such as DC voltage.

The readout is a device or component that displays data or information to the user. The readout could be a simple LED display or a complex graphical display.

A peripheral is a device or component that connects to a computer or other electronic device to provide additional functionality. Examples of peripherals include printers, scanners, and external hard drives.

A microcomputer is a type of computer that is designed to fit on a single microchip. Microcomputers are found in a wide range of devices, including smart phones, tablets, and embedded systems.

A transducer is a device that converts one form of energy to another. In electronics, transducers are commonly used to convert electrical energy into mechanical energy, or vice versa.

The processor is the central component of a computer or electronic device. The processor is responsible for executing instructions and controlling the other components of the system. The performance and capabilities of a device are largely determined by the speed and power of the processor.

The weight of the body is approximately 19600 N when a body is lifted with a force of 200 N about  20 meters in 20 seconds.

We know that distance = initial velocity*time  + (1/2) * acceleration * [tex]time^2[/tex]

Given that, the initial velocity equal to zero

distance= (1/2) * acceleration * [tex]time^2[/tex]

Also given-

distance = 20 meters

time = 20 seconds

Rearranging the formula-

20 = (1/2) * acceleration * [tex](20^2)[/tex]

20 = (1/2)   * acceleration * 400

40 = acceleration * 400

acceleration = 40/400 = 0.1 metre/[tex]sec^{2}[/tex]

Force= mass*acceleration

mass= force/acceleration

=200/0.1= 2000 Kg

But this acceleration is due to applied force but weight only involves gravitational force only.  

Since weight is defined as the force acting on an object due to gravity,

weight = mass * acceleration due to gravity

= 2000 * 9.8 (acceleration due to gravity)

= 19600 N

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The height of the building is approximately 32.34 meters.

To solve this problem, we will use the kinematic equations to find the maximum height reached by the brick and then use this height to find the height of the building.

We can start by breaking the initial velocity of the brick into its horizontal and vertical components as follows:

v₀x = v₀cos(θ) = 17cos(25°) ≈ 15.84 m/s

v₀y = v₀sin(θ) = 17sin(25°) ≈ 7.23 m/s

where θ is the angle of the initial velocity to the horizontal.

Next, we can use the following kinematic equation to find the maximum height reached by the brick:

y = y₀ + v₀yt - 1/2gt²

where y₀ is the initial height (height of the building), t is the time of flight, and g is the acceleration due to gravity (9.81 m/s²).

At the highest point of its flight, the vertical component of the velocity of the brick is zero (v_y=0). We can use this fact to find the time taken to reach maximum height:

v_y = v₀y - gt

0 = v₀y - gt_max

t_max = v₀y / g ≈ 0.738 s

We can then substitute this value of t_max into the expression for y to obtain the maximum height:

y_max = y₀ + v₀y t_max - 1/2 g t_max²

where we set y = y_max and t = t_max.

Next, we can use the total flight time of the brick (3.1 s) to find the initial height of the building:

3.1 = t_max + t_down

where t_down is the time taken by the brick to fall from the maximum height to the ground. Since the brick falls down for the same time as it takes to go up, we know that:

t_down ≈ t_max ≈ 0.738 s

Substituting this value into the equation above, we find:

3.1 ≈ 2 × 0.738 s

Finally, we can use the value of y_max obtained earlier to calculate the height of the building:

y₀ = y_max - v₀y t_down + 1/2 g t_down²

y₀ = y_max - v₀y t_max + 1/2 g t_max²

y₀ ≈ 32.34 m

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a. The water will land 0.30 meters from the wall.

b.  The water should flow at 0.042 m/s in the model.

(a)

Horizontal distance = velocity × time

h = (1/2) × g × t²

h = vertical displacement (2.30 m)

g = acceleration due to gravity (9.8 m/s²

t = time

t = √(2h/g)

t = √(2 × 2.30 / 9.8) = 0.478 s

Now, we can calculate the horizontal distance:

Horizontal distance = velocity × time

Horizontal distance = 0.628 m/s × 0.478 s = 0.30 m

The water will land less than 2 m from the wall, the space behind the waterfall will not be wide enough for a pedestrian walkway.

The answer is "No."

(b)

Actual speed of water = 0.628 m/s

Speed of water in the model = Actual speed / Scale factor

Speed of water in the model = 0.628 m/s / 15

= 0.042 m/s

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(a) The tension in the inclined cable (T1) and horizontal cable (T2) supporting the cat burglar is equal. The tension in the vertical cable (T3) is 524 N.

(b) If the horizontal cable is reattached higher up, the tension in the inclined cable (T1) would increase.

(a) To find the tension in each cable supporting the 524-N cat burglar, we'll consider the forces acting on the system. Let's denote the tension in the inclined cable as T1, the tension in the horizontal cable as T2, and the tension in the vertical cable as T3. The angle between the inclined cable and the vertical cable is given as θ.

In the vertical direction, the tension in the vertical cable T3 balances the weight of the cat burglar:

T3 - 524 N = 0

T3 = 524 N

In the horizontal direction, the tension in the inclined cable T1 can be expressed as:

T1 * cos(θ) = T2

Now, we need to determine the value of θ to calculate T1 and T2. Let's assume that θ is the given angle of θ = 0.

Substituting the angle and rearranging the equation, we have:

T1 = T2 / cos(θ)

T1 = T2 / cos(0)

T1 = T2 / 1

T1 = T2

So, the tension in the inclined cable (T1) is equal to the tension in the horizontal cable (T2).

Therefore, the tension in each cable is as follows:

T1 (inclined cable) = T2 (horizontal cable)

T1 = T2

T3 (vertical cable) = 524 N

(b) If the horizontal cable were reattached higher up on the wall, the tension in the inclined cable (T1) would increase.

The correct answer is option A.  

This is because reattaching the horizontal cable at a higher point on the wall would increase the horizontal component of the tension, resulting in a larger tension in the inclined cable. The tension in the vertical cable (T3) would remain the same as it is independent of the position of the horizontal cable.

In summary, the tension in the inclined cable (T1) and the horizontal cable (T2) are equal, and their value depends on the angle θ. The tension in the vertical cable (T3) is 524 N. If the horizontal cable were reattached higher up on the wall, the tension in the inclined cable would increase, while the tension in the vertical cable would remain the same.

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The velocity of the third piece is v₃ = -12500 kg·m/s / m₃

The law of conservation of momentum states that the total momentum before the explosion is equal to the total momentum after the explosion.

velocity of the third piece =  v₃.

The total initial momentum before the explosion = 0

The total final momentum after the explosion= 0

Initial momentum = 0 kg·m/s (since the bomb is at rest)

Final momentum = m₁v₁ + m₂v₂ + m₃v₃

m₁ = mass of the first piece = 150 kg

v₁ = velocity of the first piece = 150 m/s (to the east)

m₂ = mass of the second piece = 100 kg

v₂ = velocity of the second piece = 200 m/s (south 60° west)

m₃ = mass of the third piece = unknown

v₃ = velocity of the third piece = unknown

0 = (150 kg)(150 m/s) + (100 kg)(200 m/s)(cos(60°)) + (m₃)(v₃)

final momentum = 0 and hence  v₃ is found as :

0 = 22500 kg·m/s - 10000 kg·m/s + (m₃)(v₃)

-12500 kg·m/s = (m₃)(v₃)

v₃ = -12500 kg·m/s / m₃

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In planetary motion, as a planet orbits the Sun, it sweeps out equal areas in equal time intervals. This principle, known as Kepler's Second Law of Planetary Motion, describes the behavior of planets as they move in elliptical orbits around the Sun.

When a planet is closer to the Sun, it experiences a stronger gravitational pull, which causes it to move faster. As a result, the planet covers a larger distance in a given amount of time compared to when it is farther from the Sun. This compensates for the smaller distance, ensuring that the area swept out by the planet remains the same.

To illustrate this, imagine a line connecting the Sun and the planet, called the radius vector. As the planet moves along its orbit, the radius vector sweeps out a wedge-shaped area. The rate at which this area is swept out is constant. When the planet is closer to the Sun, it moves faster, covering more distance along its orbit in a given time. Consequently, the narrower end of the wedge is compensated by the planet's higher speed, resulting in an equal area to that covered when it is farther from the Sun.

This phenomenon is a consequence of the conservation of angular momentum in the gravitational field of the Sun and allows for a consistent distribution of the planet's orbital motion.

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(a) The average velocity of the tennis player at 0 to 1 s is  4 m/s.

(b) The average velocity of the tennis player at 0 to 4 s is -0.5 m/s.

(c) The average velocity of the tennis player at 1 to 5 s is  1 m/s.

(d) The average velocity of the tennis player at 0 to 5 s is 0.8 m/s.

The average velocity of the tennis player at the given time, is calculated by applying the formula for average velocity as follows;

average velocity = total displacement / total time

(a) The average velocity at 0 to 1 s;

average vel. = (4 m - 0 m ) / (1 s ) = 4 m/s

(b) The average velocity at 0 to 4 s;

average vel. = (-2 - 0 )m / 4 s = -0.5 m/s

(c) The average velocity at 1 to 5 s;

average vel. = (4 - 0 )m / (5 - 1) s =  1 m/s

(d) The average velocity at 0 to 5 s;

average vel. = (4 - 0 )m / (5 - 0) s =  0.8 m/s

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