### 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.

# Powerfully Fast

### Why do this problem?

This problem gives an interesting exploration into ideas concerning power and weight. It encourages accurate manipulation of numbers and units without requiring too much technical mathematics. As such, it is great for devloping numerical intuition about power.

### Possible approach

There are various parts to this question which may be considered independently. At various points, changes of units will be necessary, and part of the problem is to keep track of which units are required. There is an emphasis on numerical accuracy and manipulation, and the correct numerical results are interesting and worth discussion: at each stage ask: what do these numbers tell us? why are they interesting? is this number large, small,. surprising? how does this compare to another object that I know about? For example, the power to weight ratio of a cart horse is about 1, making it easy to work out the horsepower of various more powerful machines.

### Key questions

How does application of power change the energy of the system?
How many miles in a kilometre, feet in a centimetre, seconds in an hour, pounds in a kilogram?

### Possible extension

The extension investigation task included in the problem will yield many interesting avenues of thought

### Possible support

The hint offers a good way in to the question.