Q: An object moves in a circle of radius $$r$$ with constant speed $$v. $$What is the formula for its centripetal acceleration?

$$a_{\text{rad}} = \dfrac{v^2$}{r}$$

Question 1

A projectile is launched from ground level with an initial speed $$v_0 at an $$angle $$\$$theta_0$$ above the horizontal. Which equation gives the horizontal distance (range) the projectile travels before landing, assuming no air resistance?

Accepted Answer

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

Question 2

A football is kicked with an initial speed of $$14\ \mathrm{m/s} at an $$angle of $$60^\circ$$ above the horizontal. What is the initial vertical component of velocity?

Accepted Answer

$$v_{0y} = 14 \sin 60^\circ$$

Question 3

Which statement best describes the acceleration of an object in uniform circular motion?

Accepted Answer

The acceleration is always directed toward the center of the circle and changes the direction of velocity, not its magnitude.

Question 4

A fighter jet travels at $$v = 250\ \mathrm{m/s} in a $$horizontal circle. If the maximum tolerable radial acceleration is $$a = 6g$$, what is the maximum radius of the circle?

Accepted Answer

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

Question 5

A box car drives horizontally off a $$50.0\ \mathrm{m}$$ high cliff with an initial speed of $$18.0\ \mathrm{m/s}. $$How long is the car in the air before it lands?

Accepted Answer

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

Question 6

Which of the following correctly expresses the magnitude of a position vector $$\vec{r} in $$two dimensions?

Accepted Answer

$$|\vec{r}| = \sqrt{x^2$ + y^2$}$$

Question 7

An object moves in a circle of radius $$r$$ with constant speed $$v. $$What is the formula for its centripetal acceleration?

Accepted Answer

$$a_{	ext{rad}} = \dfrac{v^2$}{r}$$

Question 8

A grasshopper jumps from the edge of a cliff with initial speed $$v_0 at an $$angle $$	heta$$ above the horizontal. Which equation gives the initial vertical velocity component?

Accepted Answer

$$v_{0y} = v_0$ \sin 	heta$$

Question 9

In projectile motion, which component of velocity remains constant (ignoring air resistance)?

Accepted Answer

The horizontal component $$v_x$$

Question 10

A car travels around a circular track of radius $$r at $$constant speed $$v. $$What is the period $$T$$ for one complete revolution?

Accepted Answer

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

Question 11

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

Accepted Answer

It has constant magnitude but its direction continuously changes.

Question 12

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

Accepted Answer

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

Question 13

A ball is thrown horizontally from a cliff of height $$h$$ with speed $$v_0. $$What is the horizontal distance $$d it $$travels before hitting the ground?

Accepted Answer

$$d = v_0$ \sqrt{\dfrac{2h}{g}}$$

Question 14

Which of the following is true about the acceleration vector in two-dimensional motion?

Accepted Answer

It can change the speed, direction, or both of the velocity vector.

Question 15

A football kicker launches a ball with speed $$v_0 at $$angle $$\$$theta_0$$. What is the formula for the time of flight until the ball lands (assuming it lands at the same height it was kicked)?

Accepted Answer

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

Question 16

A car moves along a circular path of radius $$r at $$constant speed $$v. $$What is the direction of the acceleration vector?

Accepted Answer

Toward the center of the circle

Question 17

Which equation gives the velocity for one complete circle in terms of radius $$r$$ and period $$T$$?

Accepted Answer

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

Question 18

A grasshopper jumps with initial speed $$v_0 at$$ $$50^\circ$$ above the horizontal. What is the formula for the vertical component of its initial velocity?

Accepted Answer

$$v_{0y} = v_0$ \sin 50^\circ$$

Question 19

In two-dimensional motion, how are the $$x$$ and $$y$$ components of motion typically handled?

Accepted Answer

Independently, then connected using time as a common variable.

Chapter 3: Motion in a Plane (2-D Motion) – Study Notes

Study Guide - Practice Questions

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