### Whoosh

A ball whooshes down a slide and hits another ball which flies off the slide horizontally as a projectile. How far does it go?

### Cannon Balls

How high will a ball taking a million seconds to fall travel?

### Collision with a Vertical Spring

Coefficients of restitution meet springs in this bouncy problem

# Weekly Challenge 13: Comet Catastrophe

##### Stage: 4 and 5 Short Challenge Level:

In July 1994 the Comet Shoemaker-Levy 9 struck the planet Jupiter at a speed of around $60\textrm{ km s}^{-1}$ . Although it broke up before impact, the core of the original comet was around $5\textrm{ km}$ diameter. Its estimated density was $0.3 - 0.7\textrm{ g cm}^{-3}$.

Imagine that such a comet had struck the earth. How much would it have changed the earth's velocity relative to the sun? (Note that the mass of the earth is about $6\times 10^{24}\textrm{ kg}$).
Did you know ... ?

The mathematics of the orbits of comets and planets and cricket balls is identical and forms a large part of university applied mathematics courses.