Q: A soccer ball is kicked from the ground with an initial velocity of $$v_0 at an $$angle $$\theta$$ above the horizontal. Neglecting air resistance, which equation gives the time it takes for the ball to reach its maximum height?

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

Q: A projectile is launched with an initial velocity $$v_0 at an $$angle $$\theta$$ above the horizontal. What is the formula for the horizontal range $$R of $$the projectile (assuming it lands at the same height it was launched)?

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

Q: A paintball is fired horizontally from a gun at $$v_0 = 50$$\,\text{m/s}$$ from a height of 1.5$$\,\text{m}$$. How long does it take to hit the ground? (Use g = 9.8$$\,\text{m/s}^2$$)

$$t = \sqrt{\frac{2 \times 1.5}{9.8}}$$

Q: If a projectile is launched at an angle $$\theta$$ with initial speed $$v_0$$, what is the formula for its initial velocity components?

$$v_{0x} = v_0$ \cos \theta$$, $$v_{0y} = v_0$ \sin \theta$$

Question 1

A soccer ball is kicked from the ground with an initial velocity of $$v_0 at an $$angle $$	heta$$ above the horizontal. Neglecting air resistance, which equation gives the time it takes for the ball to reach its maximum height?

Accepted Answer

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

Question 2

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

Accepted Answer

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

Question 3

A baseball is hit and follows a parabolic trajectory. At the highest point of its flight, which of the following statements is true about its velocity?

Accepted Answer

The velocity is entirely horizontal.

Question 4

A car moves from point $$P_1 at$$ $$(4.0\,	ext{m}, 2.0\,	ext{m}) to $$point $$P_2 at$$ $$(7.0\,	ext{m}, 6.0\,	ext{m}) in$$ $$0.5\,	ext{s}. $$What is the magnitude of its average velocity?

Accepted Answer

$$10.0\,	ext{m/s}$$

Question 5

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 6

A projectile is launched horizontally from a cliff. Which statement about its acceleration is correct?

Accepted Answer

It has a constant acceleration downward equal to $$g.$$

Question 7

Given a velocity vector $$\vec{v}$$ with components $$v_x$$ and $$v_y$$, what is the magnitude of $$\vec{v}$$?

Accepted Answer

$$v = \sqrt{v_x^2$ + v_y^2$}$$

Question 8

A football is kicked at $$20\,	ext{m/s} at an $$angle of $$30^\circ$$ above the horizontal. What is the initial vertical component of its velocity?

Accepted Answer

$$20 \sin 30^\circ$$

Question 9

Which of the following is true about the acceleration of a particle moving in a plane under constant acceleration?

Accepted Answer

The acceleration vector remains constant in both magnitude and direction.

Question 10

A paintball is fired horizontally from a gun at $$v_0 = 50$$\,	ext{m/s}$$ from a height of 1.5$$\,	ext{m}$$. How long does it take to hit the ground? (Use g = 9.8$$\,	ext{m/s}^2$$)

Accepted Answer

$$t = \sqrt{\frac{2 	imes 1.5}{9.8}}$$

Question 11

If a projectile is launched at an angle $$	heta$$ with initial speed $$v_0$$, what is the formula for its initial velocity components?

Accepted Answer

$$v_{0x} = v_0$ \cos 	heta$$, $$v_{0y} = v_0$ \sin 	heta$$

Question 12

A runner moves with velocity $$\vec{v}_A$$ relative to the ground, while a train moves with velocity $$\vec{v}_B$$ relative to the ground. What is the runner's velocity relative to the train?

Accepted Answer

$$\vec{v}_A - \vec{v}_B$$

Question 13

A projectile is launched at $$v_0$$ and angle $$	heta. At $$what point in its trajectory is its speed minimum?

Accepted Answer

At the highest point.

Question 14

Which equation gives the vertical position $$y(t) of a $$projectile launched from $$y_0$$ with initial vertical velocity $$v_{0y}$$ under gravity?

Accepted Answer

$$y(t) = y_0$ + v_{0y} t - \frac{1}{2} g t^2$

Question 15

A ball is thrown with velocity $$v_0 at$$ $$45^\circ$$ above the horizontal. What is the ratio of its horizontal range to its maximum height?

Accepted Answer

$$4$$

Question 16

Which of the following statements about vector addition is correct?

Accepted Answer

Vectors are added by adding their components.

Question 17

A projectile is launched from the ground and lands at the same height. If the launch angle is increased from $$30^\circ to$$ $$60^\circ$$, what happens to the range?

Accepted Answer

It remains the same.

Question 18

Which formula gives the instantaneous acceleration vector $$\vec{a} at a $$point $$\vec{r}$$?

Accepted Answer

$$\vec{a} = \lim_{\Delta t 	o 0} \frac{\Delta \vec{v}}{\Delta t}$$

Motion in a Plane: Two-Dimensional Kinematics

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