### 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.

### Maximum Flow

Given the graph of a supply network and the maximum capacity for flow in each section find the maximum flow across the network.

# Mach Attack

##### Stage: 5 Challenge Level:
To see the shape of the wave fronts you might want to draw $5$ wave fronts emitted by the aeroplane at times $t=0, 1, 2, 3, 4, 5$. The orgin of each wave front will depend on the position of the aeroplane when it is created; once created each will be a circle whose radius grows at the speed of sound.