Q: If the ball is thrown with an initial velocity of $$v_0 at an $$angle $$\theta$$ above the horizontal, which equation gives the horizontal range $$R ($$assuming it lands at the same height it was thrown)?

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

Q: Suppose the ball is thrown from a height $$h$$ above the ground. Which equation gives the time $$t it $$takes to hit the ground (neglecting air resistance)?

$$t = \frac{v_0$ \sin \theta + \sqrt{(v_0$ \sin \$$theta)^2$$ + 2gh}}{g}$$

Question 1

Which of the following best describes the path of the ball shown in the image above?

Accepted Answer

A parabolic trajectory due to constant horizontal velocity and constant downward acceleration.

Question 2

At the apex (highest point) of the ball's trajectory in the image, what is true about the ball's velocity and acceleration?

Accepted Answer

Vertical velocity is zero, horizontal velocity is constant, acceleration is $$-9.8\ \mathrm{m/s^2$}$$ downward.

Question 3

If the ball in the image takes 2 seconds to reach the apex, how long does it take to return to the ground from the apex?

Accepted Answer

2 seconds

Question 4

What is the direction of the acceleration of the ball at all points along its path in the image?

Accepted Answer

Always downward with magnitude $$9.8\ \mathrm{m/s^2$}$$

Question 5

If the ball is thrown with an initial velocity of $$v_0 at an $$angle $$	heta$$ above the horizontal, which equation gives the horizontal range $$R ($$assuming it lands at the same height it was thrown)?

Accepted Answer

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

Question 6

At which point(s) along the ball's path is the vertical component of velocity zero?

Accepted Answer

At the apex (highest point) only

Question 7

If air resistance is neglected, what happens to the horizontal component of the ball's velocity during its flight?

Accepted Answer

It remains constant.

Question 8

Suppose the ball is thrown from a height $$h$$ above the ground. Which equation gives the time $$t it $$takes to hit the ground (neglecting air resistance)?

Accepted Answer

$$t = \frac{v_0$ \sin 	heta + \sqrt{(v_0$ \sin \$$theta)^2$$ + 2gh}}{g}$$

Question 9

If the ball is thrown at an angle of $$30^\circ$$ and another ball is thrown horizontally with the same speed, which will travel a greater horizontal distance (range) if both are released from the same height?

Accepted Answer

The ball thrown at $$30^\circ$$

Question 10

Which of the following statements is true about the horizontal and vertical accelerations of the ball at the apex of its trajectory?

Accepted Answer

Horizontal acceleration is $$0\ \mathrm{m/s^2$}$$, vertical acceleration is $$-9.8\ \mathrm{m/s^2$}$$

Physics with Calculus: 1D and 2D Motion Study Guide

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