Q: A ball is thrown horizontally from a ledge 9.0 m above the ground and lands 1.75 m from the base. What is the initial speed $$v_0 of $$the ball? (Neglect air resistance, $$g = 9.8\ \mathrm{m/s^2$})$$

$$v_0$$ = \dfrac{1.75}{\sqrt{2 \times 9.0 / 9.8}}$$

Question 1

A soccer ball is kicked from the ground with an initial speed $$v_0 at an $$angle $$\$$theta_0$$ above the horizontal. Neglecting air resistance, which of the following equations correctly gives the time t$ when the ball returns to the ground?

Accepted Answer

$$t = \dfrac{2 v_0$ \sin \$$theta_0$$}{g}$$

Question 2

A car moves along a curved path at constant speed. Which statement about its acceleration is correct?

Accepted Answer

The acceleration is always perpendicular to the velocity.

Question 3

A projectile is launched horizontally from a cliff of height $$h$$ with initial speed $$v_0. $$Neglecting air resistance, how long does it take to hit the ground?

Accepted Answer

$$t = \sqrt{\dfrac{2h}{g}}$$

Question 4

Which of the following best describes the direction of the instantaneous velocity vector of a particle moving along a curved path?

Accepted Answer

It is always tangent to the path.

Question 5

A ball is thrown with initial velocity $$v_0 at an $$angle $$\$$theta_0$$ above the horizontal. What is the horizontal range R$ of the projectile (assuming it lands at the same height it was launched)?

Accepted Answer

$$R = \dfrac{v_0$^2 \sin 2\$$theta_0$$}{g}$$

Question 6

A pilot flying at 500 km/hr must pull up to avoid a cliff. If the maximum acceleration the pilot can withstand is $$6g$$, what is the minimum radius $$R of $$the turn the pilot can make without blacking out? (Assume $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$R = \dfrac{v^2$}{6g}$$

Question 7

Which of the following statements about projectile motion (neglecting air resistance) is correct?

Accepted Answer

The horizontal and vertical motions are independent except for sharing the same time of flight.

Question 8

A ball is thrown straight up with velocity $$v_0. At $$the top of its path, which of the following is true?

Accepted Answer

The velocity is zero, but the acceleration is $$-g.$$

Question 9

A cyclist rides east at $$5\ \mathrm{m/s}$$ relative to the ground, and a train moves east at $$20\ \mathrm{m/s}$$ relative to the ground. What is the velocity of the cyclist relative to the train?

Accepted Answer

$$-15\ \mathrm{m/s}$$

Question 10

Which of the following is the correct expression for the centripetal (radial) acceleration $$a_{\mathrm{rad}} of an $$object moving at speed $$v in a $$circle of radius $$R$$?

Accepted Answer

$$a_{\mathrm{rad}} = \dfrac{v^2$}{R}$$

Question 11

A ball is thrown horizontally from a ledge 9.0 m above the ground and lands 1.75 m from the base. What is the initial speed $$v_0 of $$the ball? (Neglect air resistance, $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$v_0$$ = \dfrac{1.75}{\sqrt{2 	imes 9.0 / 9.8}}$$

Question 12

Which of the following best describes the acceleration vector for a particle moving along a curved path with increasing speed?

Accepted Answer

It points ahead of the normal to the path, having both tangential and normal components.

Question 13

A ball bounces repeatedly, reaching lower heights after each bounce. What is the main reason for the decrease in height?

Accepted Answer

The ball loses energy with each bounce due to non-conservative forces.

Question 14

Which of the following is the correct vector equation for the position vector $$\vec{r} of a $$particle in three dimensions?

Accepted Answer

$$\vec{r} = x \hat{i} + y \hat{j} + z \hat{k}$$

Question 15

A car is slowing down while rounding a curve. Which statement about its acceleration is correct?

Accepted Answer

The acceleration has both a component perpendicular to the velocity (changing direction) and a component opposite to the velocity (slowing down).

Question 16

Which of the following is the correct formula for the average velocity $$\vec{v}_{\mathrm{av}}$$ between two points?

Accepted Answer

$$\vec{v}_{\mathrm{av}} = \dfrac{\Delta \vec{r}}{\Delta t}$$

Question 17

A projectile is launched at an angle $$\$$theta_0$$ with initial speed v_0$. What are the initial velocity components?

Accepted Answer

$$v_{0x} = v_0$ \cos \$$theta_0$$, v$$_{0y} = $$v_0$$ \sin \$$theta_0$$

Question 18

Which of the following is true for uniform circular motion?

Accepted Answer

The acceleration vector always points toward the center of the circle.

Question 19

A train moves east at $$30\ \mathrm{m/s}$$ relative to the ground. A passenger walks west at $$2\ \mathrm{m/s}$$ relative to the train. What is the passenger's velocity relative to the ground?

Accepted Answer

$$28\ \mathrm{m/s}$$\ east

Motion in Two or Three Dimensions: Study Notes

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