Question 1

A baseball is hit and follows a parabolic trajectory. If air resistance is neglected, which of the following statements about its horizontal and vertical motions is correct?

Accepted Answer

The horizontal velocity remains constant, while the vertical velocity changes due to gravity.

Question 2

A cyclist moves around a circular track at a constant speed. Which statement best describes the cyclist's acceleration?

Accepted Answer

The cyclist is accelerating because the direction of velocity is changing.

Question 3

A projectile is launched from the ground at an angle $$\$$theta_0$$ with initial speed v_0$. What is the formula for the maximum range R$ (assuming the initial and final elevations are the same and neglecting air resistance)?

Accepted Answer

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

Question 4

A paintball is fired horizontally from a height of $$1.50\,\mathrm{m}$$ with an initial speed of $$75.0\,\mathrm{m/s}. $$Neglecting air resistance, how far will it travel horizontally before hitting the ground?

Accepted Answer

About $$29.2\,\mathrm{m}$$

Question 5

Which of the following best describes the direction of the acceleration vector for an object in uniform circular motion?

Accepted Answer

It points toward the center of the circle.

Question 6

A car drives in a straight line at $$20\,\mathrm{m/s} in a $$direction $$30^\circ$$ East of North. How long will it take the car to travel $$60\,\mathrm{m}$$ East of its starting location?

Accepted Answer

$$t = \dfrac{60}{20 \sin 30^\circ}$$

Question 7

Which equation gives the vertical position $$y of a $$projectile launched at angle $$\$$theta_0$$ with initial speed v_0$ after time t$?

Accepted Answer

$$y = v_0$ \sin \$$theta_0$$ \cdot t - \dfrac{1}{2} g t^2$

Question 8

A ball is dropped from rest and another is fired horizontally from the same height at the same time. Neglecting air resistance, which ball hits the ground first?

Accepted Answer

Both hit the ground at the same time.

Question 9

Which of the following is the correct expression for the centripetal acceleration $$a_c of an $$object moving at speed $$v in a $$circle of radius $$R$$?

Accepted Answer

$$a_c = \dfrac{v^2$}{R}$$

Question 10

A projectile is launched at $$45^\circ$$ with initial speed $$v_0. $$What is the maximum range $$R_{max} it $$can achieve (neglecting air resistance)?

Accepted Answer

$$R_{max} = \dfrac{v_0$^2}{g}$$

Question 11

If a baseball game were played on the Moon, how would the vertical drop of a horizontally thrown pitch compare to that on Earth?

Accepted Answer

The drop would be less on the Moon because gravity is weaker.

Question 12

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

Accepted Answer

It is always tangent to the path.

Question 13

A passenger walks forward in a train moving east at $$10\,\mathrm{m/s}$$, with the passenger walking at $$2\,\mathrm{m/s}$$ relative to the train. What is the passenger's velocity relative to the ground?

Accepted Answer

$$12\,\mathrm{m/s}$$\ east

Question 14

Which of the following is true about the independence of motion in the $$x$$ and $$y$$ directions for projectile motion?

Accepted Answer

The motion in the $$x$$ direction is independent of the motion in the $$y$$ direction.

Question 15

A projectile is launched at an angle $$\$$theta_0$$ with initial speed v_0$. What is the formula for the maximum height H$ reached by the projectile?

Accepted Answer

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

Question 16

Which of the following is a correct statement about average acceleration?

Accepted Answer

It is the change in velocity divided by the time interval.

Question 17

A carnival ride makes one complete circle in $$4.0\,\mathrm{s}$$ with a radius of $$6.0\,\mathrm{m}. $$What is the magnitude of the centripetal acceleration?

Accepted Answer

$$a_c = \dfrac{(2\pi \cdot 6.0 / 4.0)^2$}{6.0}$$

Question 18

Which of the following is true about the effect of air resistance on projectile motion?

Accepted Answer

Air resistance decreases the range and maximum height.

Chapter 3: Motion in Two or Three Dimensions – Study Notes

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