Q: A circus performer is launched from a cannon as shown in the first image. If the performer is launched at an angle $$\theta$$ with an initial speed $$v_0$$, which of the following equations correctly gives the time $$t it $$takes for the performer to reach the maximum height? (Neglect air resistance and use $$g$$ for the acceleration due to gravity.)

$$t = \frac{v_0$ \sin \theta}{g}$$

Q: A projectile is launched from the ground and lands at the same height. Which of the following equations gives the range $$R of $$the projectile?

$$R = \frac{v_0$^2 \sin 2\theta}{g}$$

Q: In the third image, a person throws an object toward a ship. If the object is thrown with an initial velocity $$v_0 at an $$angle $$\theta$$ and lands at the same height, what is the total time of flight?

$$t = \frac{2 v_0$ \sin \theta}{g}$$

Q: A ball is thrown with an initial velocity of $$20\ \mathrm{m/s} at an $$angle of $$30^\circ$$ above the horizontal. What is the maximum height reached by the ball? (Use $$g = 9.8\ \mathrm{m/s^2$})$$

$$H = \frac{(20 \sin 30^\$$circ)^2$$}{2 \times 9.8}$$

Question 1

A circus performer is launched from a cannon as shown in the first image. If the performer is launched at an angle $$	heta$$ with an initial speed $$v_0$$, which of the following equations correctly gives the time $$t it $$takes for the performer to reach the maximum height? (Neglect air resistance and use $$g$$ for the acceleration due to gravity.)

Accepted Answer

$$t = \frac{v_0$ \sin 	heta}{g}$$

Question 2

In the second image, a soccer player kicks a ball over a wall toward the goal. If the ball is kicked with an initial velocity $$v_0 at an $$angle $$	heta$$ above the horizontal, which of the following best describes the horizontal component of the ball’s velocity?

Accepted Answer

$$v_{0x} = v_0$ \cos 	heta$$

Question 3

A projectile is launched from the ground and lands at the same height. Which of the following equations gives the range $$R of $$the projectile?

Accepted Answer

$$R = \frac{v_0$^2 \sin 2	heta}{g}$$

Question 4

In the third image, a person throws an object toward a ship. If the object is thrown with an initial velocity $$v_0 at an $$angle $$	heta$$ and lands at the same height, what is the total time of flight?

Accepted Answer

$$t = \frac{2 v_0$ \sin 	heta}{g}$$

Question 5

A rabbit’s position as a function of time is given by $$x(t) = 2t + 3$$ and $$y(t) = t^2$. What is the rabbit’s velocity vector at t = 4$ s?

Accepted Answer

$$\vec{v} = 2\hat{i} + 8\hat{j}$$

Question 6

Which of the following statements about projectile motion is correct?

Accepted Answer

The horizontal velocity remains constant if air resistance is neglected.

Question 7

A ball is thrown with an initial velocity of $$20\ \mathrm{m/s} at an $$angle of $$30^\circ$$ above the horizontal. What is the maximum height reached by the ball? (Use $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$H = \frac{(20 \sin 30^\$$circ)^2$$}{2 	imes 9.8}$$

Question 8

If a projectile is launched at an angle $$	heta$$ and lands at the same height, at what angle is the range maximized?

Accepted Answer

$$45^\circ$$

Question 9

A vector has components $$A_x = 3$$ and $$A_y = 4. $$What is the magnitude and direction (angle with the x-axis) of the vector?

Accepted Answer

Magnitude: $$5$$, Angle: $$\arctan(\frac{4}{3})$$

Question 10

Which of the following best describes the acceleration of a projectile in free fall (neglecting air resistance)?

Accepted Answer

Constant and directed downward with magnitude $$g$$

Question 11

A ball is thrown horizontally from a cliff with speed $$v_0. $$Which equation gives the time $$t it $$takes to hit the ground from height $$h$$?

Accepted Answer

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

Question 12

A car moves in a circular path at constant speed. Which of the following statements is true?

Accepted Answer

The velocity is always tangent to the path.

Question 13

A rabbit’s position is given by $$\vec{r}(t) = (4t)\hat{i} + (t^2$)\hat{j}. $$What is the acceleration vector at $$t = 3 s$$?

Accepted Answer

$$\vec{a} = 0\hat{i} + 2\hat{j}$$

Question 14

Which of the following is the correct expression for the average velocity $$\vec{v}_{avg}$$ between times $$t_1$$ and $$t_2$$?

Accepted Answer

$$\vec{v}_{avg} = \frac{\vec{r}(t_2$) - \vec{r}(t_1$)}{t_2$ - t_1$}$$

Question 15

A projectile is launched at $$20\ \mathrm{m/s} at$$ $$45^\circ$$ above the horizontal. What is the horizontal range? (Use $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$R = \frac{20^2$ \sin 90^\circ}{9.8}$$

Question 16

Which of the following is true about the instantaneous velocity vector of a particle moving along a curved path?

Accepted Answer

It is always tangent to the trajectory.

Question 17

A projectile is launched from the ground at an angle $$	heta$$ with initial speed $$v_0. $$Which of the following is the correct expression for the maximum height $$H$$?

Accepted Answer

$$H = \frac{v_0$^2 \sin^2$ 	heta}{2g}$$

Question 18

A ball is thrown at an angle $$	heta$$ with initial speed $$v_0. $$Which of the following is true about the vertical component of the velocity at the highest point?

Accepted Answer

It is zero.

Question 19

A projectile is launched horizontally from a height $$h$$ with speed $$v_0. $$What is the horizontal distance traveled before hitting the ground?

Accepted Answer

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

Kinematics in Two and Three Dimensions: Vectors and Projectile Motion

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