Q: A man stands on the top of a 15.0-m-tall building and throws a rock with a velocity of 30.0 m/s at an angle of 33.0° above the horizontal. What is the vertical component of the initial velocity $$v_{0y}$$?

$$v_{0y} = 30.0 \times \sin(33.0$$^{\circ}$$)$$

Question 1

A man stands on the top of a 15.0-m-tall building and throws a rock with a velocity of 30.0 m/s at an angle of 33.0° above the horizontal. What is the vertical component of the initial velocity $$v_{0y}$$?

Accepted Answer

$$v_{0y} = 30.0 	imes \sin(33.0$$^{\circ}$$)$$

Question 2

For the same scenario, what is the maximum height above the roof reached by the rock?

Accepted Answer

$$h_{max} = \frac{v_{0y}^2}{2g}$$

Question 3

A bomber flies horizontally at 275 mile/hr at an altitude of 9000 ft. At what viewing angle $$\phi$$ from the bomber to the target should the bomb be dropped?

Accepted Answer

$$\phi = \arctan\left(\frac{H}{R}\right)$$

Question 4

In uniform circular motion, what is the direction of the acceleration vector?

Accepted Answer

Toward the center of the circle

Question 5

What is the formula for the magnitude of centripetal acceleration $$a in $$terms of speed $$v$$ and radius $$r$$?

Accepted Answer

$$a = \frac{v^2$}{r}$$

Question 6

Earth rotates once around its axis every 24 h. If the mean radius of the earth is $$6.4 	imes 10^6$ m, what is the speed of a point on the equator?

Accepted Answer

$$v = \frac{2\pi r}{T}$$

Question 7

A pendulum swings back and forth, reaching a maximum angle of 45° from the vertical. As it passes through the lowest point, what is the direction of its acceleration?

Accepted Answer

Straight down

Question 8

If a person is walking at 1.0 m/s on a train that is moving at 3.0 m/s, what is their velocity relative to the ground?

Accepted Answer

$$v_{person/ground} = v_{person/train} + v_{train/ground}$$

Question 9

For uniform circular motion, what is the relationship between the period $$T$$ and the speed $$v$$?

Accepted Answer

$$v = \frac{2\pi r}{T}$$

Question 10

A rock is thrown from a building as shown in the diagram. If air resistance is ignored, which equation best describes the vertical position $$y as a $$function of time $$t$$?

Accepted Answer

$$y = y_0$ + v_{0y} t - \frac{1}{2} g t^2$

Question 11

A carnival ride spins passengers in a circle at constant speed. What causes the passengers to feel 'pushed' outward?

Accepted Answer

The inertia of their bodies resisting the centripetal acceleration

Question 12

A projectile is launched from a height $$h$$ with initial velocity $$v_0 at $$angle $$\$$alpha_0$$. What is the horizontal range R$ from the base of the building to where it lands?

Accepted Answer

$$R = v_{0x} t_{total}$$, where $$t_{total} is $$the time to hit the ground

Question 13

Which of the following best describes the velocity vector in uniform circular motion?

Accepted Answer

It is tangent to the circle at every point

Question 14

A cyclist observes a passenger walking inside a train. Which equation gives the passenger's velocity relative to the cyclist?

Accepted Answer

$$v_{P/A} = v_{P/B} + v_{B/A}$$

Question 15

If the period of revolution $$T$$ for a particle in uniform circular motion is doubled, what happens to the centripetal acceleration $$a$$?

Accepted Answer

$$a$$ decreases by a factor of 4

Question 16

A projectile is launched horizontally from a height $$H. $$What is the time it takes to reach the ground?

Accepted Answer

$$t = \sqrt{\frac{2H}{g}}$$

Question 17

Which of the following statements about acceleration in uniform circular motion is correct?

Accepted Answer

Acceleration is always directed toward the center of the circle

Question 18

A rock is thrown from a building as shown. If the initial velocity is $$v_0 at $$angle $$\$$alpha_0$$, what is the horizontal component of the velocity v$$_{0x}$$?

Accepted Answer

$$v_{0x} = v_0$ \cos(\$$alpha_0$$)$$

Question 19

In the context of relative motion, which frame of reference would measure the highest velocity for a passenger walking inside a moving train?

Accepted Answer

A stationary observer on the ground

Motion in Two or Three Dimensions: Kinematics and Uniform Circular Motion

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