### Ball Bearings

If a is the radius of the axle, b the radius of each ball-bearing, and c the radius of the hub, why does the number of ball bearings n determine the ratio c/a? Find a formula for c/a in terms of n.

### Overarch 2

Bricks are 20cm long and 10cm high. How high could an arch be built without mortar on a flat horizontal surface, to overhang by 1 metre? How big an overhang is it possible to make like this?

### Stonehenge

Explain why, when moving heavy objects on rollers, the object moves twice as fast as the rollers. Try a similar experiment yourself.

# Cushion Ball

##### Stage: 5 Challenge Level:

Why do this problem?
The context is interesting and this can be an exercise in finding distances using coordinates. This process, of repeatedly reflecting the snooker table in its sides, occurs in many areas of advanced mathematics and for a simple introduction see the article In Space Do All Roads Lead Home?

Possible approach
Use the hint.

Key question
We know the ball bounces of the cushion at an equal angle so how do we use this fact to find the right point on the cushion to aim for?

Possible support
See Snookered.