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

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

Q: A football is kicked at $$v_0 = 20$ m/s at 45$$^\circ$$ above the horizontal. What is the maximum height reached by the ball?

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

Q: A ball is thrown with velocity $$v_0 at $$angle $$\theta. $$What is the time of flight until it returns to the same vertical level?

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

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 of the following correctly describes the acceleration of the ball during its flight?

Accepted Answer

The acceleration is $$a_x = 0$$ and $$a_y = -g at $$all times.

Question 2

Given a position vector $$\vec{r} = x \hat{i} + y \hat{j}$$, what is the magnitude of $$\vec{r}$$?

Accepted Answer

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

Question 3

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

Accepted Answer

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

Question 4

Which statement best describes the instantaneous velocity vector of a particle moving along a curved path in the $$xy-$$plane?

Accepted Answer

It is always tangent to the path at the particle's position.

Question 5

A projectile is launched with initial velocity components $$v_{0x}$$ and $$v_{0y}. $$What is the velocity in the $$y-$$direction at time $$t$$?

Accepted Answer

$$v_y(t) = v_{0y} - gt$$

Question 6

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

Accepted Answer

$$5.0 m/s$$

Question 7

Which of the following is true about the acceleration vector for a particle moving in a plane?

Accepted Answer

It can change due to a change in magnitude and/or direction of velocity.

Question 8

A projectile is fired horizontally from a cliff with speed $$v_0. $$What is its vertical displacement after time $$t$$?

Accepted Answer

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

Question 9

If a vector $$\vec{A}$$ has components $$A_x = 3$$ and $$A_y = 4$$, what is the angle $$	heta it $$makes with the $$x-$$axis?

Accepted Answer

$$	heta = \arctan(4/3)$$

Question 10

A paintball is fired at $$v_0 = 50$ m/s at an angle $$	heta = 30^\circ$$ above the horizontal. What is the initial vertical component of velocity?

Accepted Answer

$$v_{0y} = v_0$ \sin(30^\circ)$$

Question 11

A football is kicked at $$v_0 = 20$ m/s at 45$$^\circ$$ above the horizontal. What is the maximum height reached by the ball?

Accepted Answer

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

Question 12

Which of the following best describes the method for subtracting two vectors $$\vec{A}$$ and $$\vec{B}$$?

Accepted Answer

Add $$\vec{A}$$ and the negative of $$\vec{B}.$$

Question 13

A runner moves with velocity $$\vec{v}_1$$ relative to the ground, while the ground moves with velocity $$\vec{v}_2$$ relative to a train. What is the runner's velocity relative to the train?

Accepted Answer

$$\vec{v}_1 - \vec{v}_2$$

Question 14

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

Accepted Answer

At the highest point of the trajectory.

Question 15

Which equation gives the position in the $$x-$$direction for a projectile launched with initial velocity $$v_{0x}$$?

Accepted Answer

$$x(t) = x_0$ + v_{0x} t$$

Question 16

A ball is thrown with velocity $$v_0 at $$angle $$	heta. $$What is the time of flight until it returns to the same vertical level?

Accepted Answer

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

Question 17

A projectile is launched at $$v_0$$ and $$	heta. $$What is the formula for its velocity vector at time $$t$$?

Accepted Answer

$$\vec{v}(t) = v_0$ \cos 	heta \hat{i} + (v_0$ \sin 	heta - g t) \hat{j}$$

Question 18

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

Accepted Answer

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

Motion in a Plane – Study Notes (College Physics, Chapter 3)

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