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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?

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Stonehenge

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

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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.

Making More Tracks

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

We know the coordinates of the rear wheel. We need to find the coordinates of the front wheel. To do this think about the instantaneous direction of travel of the rear wheel of the bike at any moment in time as it travels along its curve. How far away and in what direction is the front wheel located?

For the conjecturing, always relate back to the physical experience of riding a bike.