Final answer:
An athlete would need to be running at 0.91 times the speed of light for a 100-m race to look 100 yards long. This demonstrates the principle of length contraction in special relativity, an effect not observed in ordinary life due to much lower achievable speeds.
Step-by-step explanation:
To determine how fast an athlete would need to be running for a 100-metre race to appear 100 yards long, we must understand the concept of length contraction in special relativity, which is a part of modern physics.
Length contraction is given by the formula L = L0 / √(1 - v^2/c^2) where L is the contracted length, L0 is the proper length, v is the velocity of the moving object, and c is the speed of light. To find the velocity that makes a 100-m look 100 yd, we convert 100 yd to meters (1 yard = 0.9144 meters, so 100 yd = 91.44 meters), and then find the velocity v that satisfies the relationship 91.44 m = 100 m / √(1 - v^2/c^2).
By solving this equation for v, we can determine that the correct answer is (a) 0.91 times the speed of light. This high velocity is way beyond the realm of human capability and demonstrates that relativistic effects such as length contraction are not observed in ordinary circumstances because the speeds involved are much smaller than the speed of light. If relativistic effects were easily observable, we would regularly see different lengths of objects as they move relative to us, even in everyday situations