Question

Modern Physics: Special Relativity

An athlete knows that if a time interval on a moving spacecraft is measured from Earth the time will be greater than would be measured on the spacecraft. They propose to set a world record 100 m dash time by having the time measured by an observer on a moving spacecraft. (The race will still take place on Earth.) Will this plan work? Provide a mathematical justification.

Answer 1

From the spacecraft's point of view, the Earth is moving at a speed v

Suppose the relative speed of Earth and Spacecraft be

Now suppose the athlete takes 10 seconds to complete 100 m race as measured on Earth.

Then the time taken to complete the race as measured by someone on the spacecraft is

This time measured by the moving spacecraft is larger than the time measured on Earth.

Hence the athlete's plan to set a world record will NOT work