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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?

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.

Differential Electricity

Age 16 to 18 Challenge Level:

 

V represents the voltage drop across the parallel combination of the capacitor (C) and resistor (R). Find the differential equation that V obeys in terms of $V_0$ and its derivatives.

Make up some realistic constants for a capacitor. Can you solve the resulting differential equation?