### Ball Bearings

If a is the radius of the axle, b the radius of each ball-bearing, and c the radius of the hub, why does the number of ball bearings n determine the ratio c/a? Find a formula for c/a in terms of n.

### Far Horizon

An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?

### Air Routes

Find the distance of the shortest air route at an altitude of 6000 metres between London and Cape Town given the latitudes and longitudes. A simple application of scalar products of vectors.

# Alternative Record Book

##### Stage: 4 and 5 Challenge Level:

In the Olympic and Paralympic Games, medals are awarded for the best performances in each event. But what if we used different criteria for writing an alternative record book?

Investigate some of the questions below to write your own Alternative Record Book.

You will need to do some research to answer these questions, and you will need to make some estimations and approximations. You may also need to refine the questions to make them more precise. If you can't determine an exact value for certain contexts, you could try to compute upper or lower bounds to allow you to compare.

In which Olympic or Paralympic event does:

• A human travel fastest? How fast?

• An object travel fastest? How fast?

• An object travel highest? How high?

• A human expend the most calories? How many?

• A human react fastest? How fast?

• A human experience the greatest acceleration or deceleration? How much?

• An object experience the greatest forces, stresses or strains? How much?

Send us your thoughts about which events should be included in the Alternative Record Book, together with your evidence and calculations.

Can you think of any other categories to include in your Alternative Record Book?

You may wish to do some experiments and create an Alternative Record Book for your own school and its athletes.