### Take a Message Soldier

A messenger runs from the rear to the head of a marching column and back. When he gets back, the rear is where the head was when he set off. What is the ratio of his speed to that of the column?

### Alternative Record Book

In which Olympic event does a human travel fastest? Decide which events to include in your Alternative Record Book.

# Dangerous Driver?

##### Age 16 to 18 Challenge Level:

We had two very interesting solutions, which were beautifully presented Word documents -- click below to read them

Michael from Ecclesbourne
Michael believes that the penalty could not reasonably be rejected as the situation stands -- more information will be required about the specific car in question because, quite rightly, acceleration will not be constant in a real situation.

Henry, from Elizabeth College
Henry carefully converted all of the units and performed a calculation based on constant acceleration and various equations of mechanics. Based on these assumptions, he concludes that the car could be going as fast as 41m/s. This is greater that the speed that the camera recorded and that the case should not be dismissed on mathematical grounds.

Steve notes
In reality I wondered if constant power produced by the car might be a more solid starting point for a calculation. In principle this could be inferred from the solid data point of acceleration from 0 to 96 km/h in 10.5 seconds. A big unknown would be the retarding effect of wind resistance. Another big unknown would be the road configuration. Is it curved, straight, flat or up/downhill?

Patrick sent us his solution, which considers how air resistance might affect the problem.

He used the formula for air resistance, $F_{air} =\frac 12 A C_d D v^2$, where $A$ is the cross-sectional area of the car, $C_d$ is a constant saying how resistive air is and $D$ is the density of the air.

He also used the chain rule to write acceleration as:
$\frac{dv}{dt} = \frac{dx}{dt} \frac{dv}{dx} = v \frac{dv}{dx}$