Q: A soccer ball is kicked from ground level with an initial speed $$v_0 at an $$angle $$\theta$$ with respect to the horizontal. What is the symbolic expression for the time $$t it $$takes to reach a wall a distance $$L$$ away?

$$t = \dfrac{L}{v_0$ \cos\theta}$$

Q: A projectile is launched from the ground with speed $$v_0 at $$angle $$\theta. $$What is the maximum height $$H it $$reaches above the ground?

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

Q: A projectile is launched from the ground with initial speed $$v_0 at $$angle $$\theta. $$What is the total time of flight before it lands back on the ground?

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

Q: A projectile is launched from the ground with speed $$v_0 at $$angle $$\theta. $$What is the range $$R ($$horizontal distance traveled before landing)?

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

Question 1

A projectile is launched from the ground with an initial speed $$v_0 at an $$angle $$	heta$$ above the horizontal. Which of the following equations correctly gives the horizontal position $$x as a $$function of time $$t ($$assuming $$x_0 = 0$ and no air resistance)?

Accepted Answer

$$x = v_0$ \cos	heta \ t$$

Question 2

A soccer ball is kicked from ground level with an initial speed $$v_0 at an $$angle $$	heta$$ with respect to the horizontal. What is the symbolic expression for the time $$t it $$takes to reach a wall a distance $$L$$ away?

Accepted Answer

$$t = \dfrac{L}{v_0$ \cos	heta}$$

Question 3

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

Accepted Answer

$$a_y = -g$$

Question 4

Given the kinematic equation $$y = y_0$ + v_{0y} t + \frac{1}{2} a_y t^2$, what is the vertical position y$ of a projectile at time t$ if it is launched from the ground (y_0$ = 0) $$with initial vertical velocity $$v_{0y}$$ and $$a_y = -g$$?

Accepted Answer

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

Question 5

A hunter aims directly at a monkey hanging from a branch. At the instant the hunter fires, the monkey lets go and begins to fall. Assuming the dart is not affected by air resistance, what happens?

Accepted Answer

The dart hits the monkey.

Question 6

Which equation gives the vertical velocity $$v_y of a $$projectile at time $$t if it is $$launched with initial vertical velocity $$v_{0y}$$ and acceleration $$a_y$$?

Accepted Answer

$$v_y = v_{0y} + a_y t$$

Question 7

A projectile is launched from the ground with speed $$v_0 at $$angle $$	heta. $$What is the maximum height $$H it $$reaches above the ground?

Accepted Answer

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

Question 8

Which of the following is the correct kinematic equation for the horizontal position $$x of an $$object under constant acceleration $$a_x$$?

Accepted Answer

$$x = x_0$ + v_{0x} t + \frac{1}{2} a_x t^2$

Question 9

A ball is thrown horizontally from a cliff with speed $$v_0. $$How long does it take to hit the ground if the height of the cliff is $$h$$?

Accepted Answer

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

Question 10

A projectile is launched from the ground with initial speed $$v_0 at $$angle $$	heta. $$What is the total time of flight before it lands back on the ground?

Accepted Answer

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

Question 11

A projectile is launched from the ground with speed $$v_0 at $$angle $$	heta. $$What is the range $$R ($$horizontal distance traveled before landing)?

Accepted Answer

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

Question 12

Which of the following statements about projectile motion is correct?

Accepted Answer

The horizontal acceleration is zero.

Question 13

A ball is thrown at an angle $$	heta$$ with initial speed $$v_0. At $$the highest point of its trajectory, which of the following is true?

Accepted Answer

The vertical velocity is zero.

Question 14

A projectile is launched from the ground with initial speed $$v_0 at $$angle $$	heta. $$What is the vertical component of its initial velocity?

Accepted Answer

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

Question 15

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

Accepted Answer

$$v = \sqrt{v_0$^2 + 2gh}$$

Motion in Two Dimensions: Kinematics and Projectile Motion

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