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 Appendix IIl

Planning Exercises

Exercise 1
Consider a table tennis ball bouncing on a hard horizontal surface. The height to which the ball bounces, h2, obviously depends on the height from which it is dropped, h1.
Predict a possible mathematical relation between h2 and h1 giving justification for your answer. Estimate the maximum value of h1 for which you expect the relation to be valid (give an explanation of your estimate).
Also, say what graph you would plot in order to verify the relation.
Exercise 2
What are the factors which you would expect to determine the time taken for the temperature of a cup of coffee to fall (say) 5°C ?
Describe an experiment to investigate at least one of these factors.
Exercise 3
Imagine a plastic water bottle which has a small hole, of diameter d, in the bottom.

a) If water is put in the bottle, how would you expect the volume of water "escaping" per second, V/t, to depend on:
 i) the height of water, h (with d constant) and ii) the diameter of the hole (with h constant)? To answer, give sketch graphs of V/t against h and V/t against d.
b) Describe briefly an experiment to verify the relation between V/t and h.
Exercise 4
Describe an experiment to find the best angle at which a ball should be thrown in order to have the maximum possible range an a horizontal plane (on a day when there is no wind). Make a prediction as to what angle you would expect to be the best and justify your prediction.