Ancient Greek long jump with weights · CAP 2004 #P3
Physics · mechanics
Problem
The long jump as an Olympic sport dates back at least as far as 700 BC. Unlike in the modern Olympics, it was practised not only from a running start, but also from a standing start. The length of a jump was measured (as it still is) from the point where the back of the feet touched the ground on landing. Paintings on ancient Greek vases depict athletes jumping from a standing start while holding compact weights in both hands. Examples of these have been dug up by archaeologists, and typical ones, made of stone or lead, each have a mass of around 3 kg.
(a) Write a short paragraph explaining qualitatively how athletes could boost their performance, i.e. jump further from a standing start, by carrying such weights. More precisely, describe what they would have done with the weights during the jump. You can accept that, as biomechanics research has shown, a loaded body could take off at the same speed and angle as an unloaded one.
(b) Estimate by how much the length of a 3 m jump could be increased for a 65 kg athlete jumping at an angle of 50°. Remember that this takes place from a standing start, not a running start like today's long jump. You can take the centre of mass of the body to be at a height of 1 m above the ground at takeoff.