A standard Canadian football field is 100 m long and 60 m wide.A UFO streaks from one end of the field to the other at a speed of 0.6c relative to the players on the field.The aliens in the UFO decide to watch the game on television as they head off toward Jupiter.The game begins at 1:30 p.m.and ends at 4:30 p.m.according to earthbound broadcasters.The elapsed time for the game according to the aliens is

Question

Quizplus · Accepted Answer

The distance traveled by the UFO is 100 meters (the length of the field). The speed of the UFO relative to the players on the field is given as 0.6c. We need to find the time interval as measured by the aliens in the UFO.

The time dilation formula is given by:

t' = t / γ

where t' is the time interval measured by someone in the UFO, t is the time interval measured by someone on the field, and γ is the Lorentz factor given by:

γ = 1 / sqrt(1 - v^2/c^2)

where v is the speed of the UFO and c is the speed of light.

Substituting the values, we get:

γ = 1 / sqrt(1 - 0.6^2) ≈ 1.25

t' = (4.5 - 1.5) / γ = 3 / 1.25 = 2.4 hours

So, the elapsed time for the game according to the aliens is 2.4 hours, which is closest to option D).

A Standard Canadian Football Field Is 100 M Long and 60