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

Stage: 5 Challenge Level:
This problem uses the concept of power being the rate of work.

Thus, if all of the work is converted into kinetic energy then we will have
$$P = \frac{d}{dt}\left(\frac{1}{2}mv^2\right)$$
Note that you can integrate this expression!