# Bouncy Ball

A ball is dropped vertically, falls through a height h and strikes a ramp that is inclined 45 degrees to the horizontal. The ball undergoes perfectly elastic collision.

(a) How far down the ramp does the ball land after the first bounce?

(b) Calculate the time $$t$$ between the first bounce and the second bounce.

(c) Calculate the speed of impact, $$v_0$$ and the angle $$\theta$$ that the ball makes with the vertical at the second impact.

(d) For the second and third bounces, find the distance the ball travels down the ramp (in term of $$h$$), the time in the air (in terms of $$t$$), and the speed at impact (in term of $$v_0$$) and the tangent of the angle with the vertical at impact.

(e) Generalize your answers to the nth bounce for the quantities in part (e).

Note by A Brilliant Member
1 year, 11 months ago

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold
- bulleted- list
• bulleted
• list
1. numbered2. list
1. numbered
2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1paragraph 2

paragraph 1

paragraph 2

[example link](https://brilliant.org)example link
> This is a quote
This is a quote
    # I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
MathAppears as
Remember to wrap math in $$...$$ or $...$ to ensure proper formatting.
2 \times 3 $$2 \times 3$$
2^{34} $$2^{34}$$
a_{i-1} $$a_{i-1}$$
\frac{2}{3} $$\frac{2}{3}$$
\sqrt{2} $$\sqrt{2}$$
\sum_{i=1}^3 $$\sum_{i=1}^3$$
\sin \theta $$\sin \theta$$
\boxed{123} $$\boxed{123}$$