Question

Relativity Blitz - I Two pole vaulters, Bill and Jill, are running on a track in opposite directions, each going with speed of 0.700c and carrying their poles horizontally, aligned with their direction of motion. Both poles have a proper (rest) length of 7.50 meters. (a) What is the apparent length of the poles to a spectator sitting next to the track? (b) From Bill's perspective, what is the apparent length of Jill's pole? (c) As Jill reaches the end of her run, she plants her pole and vaults so that the pole becomes vertical. According to Bill, who is still running, what is the length of Jill's pole in this orientation?

Answer 1

The apparent length of the poles to a spectator next to the track can be calculated using the principle of length contraction in special relativity. From Bill's perspective, the apparent length of Jill's pole can also be calculated using the same principle. As Jill plants her pole and makes it vertical, it will appear shorter to Bill.

Step-by-step explanation:

(a) According to the principle of length contraction in special relativity, the apparent length of an object moving at relativistic speeds appears shorter to an observer in a different reference frame. The formula for length contraction is given by L' = L√(1 - v^2/c^2), where L is the proper (rest) length, L' is the apparent length, v is the relative velocity, and c is the speed of light. Using this formula, the apparent length of the poles to a spectator sitting next to the track can be calculated as follows:

L' = 7.50m √(1 - (0.700c)^2 / c^2)

where c is the speed of light. (b) From Bill's perspective, the apparent length of Jill's pole can be calculated using the same formula. (c) As Jill reaches the end of her run and plants her pole to make it vertical, the pole will appear shorter to Bill due to the length contraction effect.