A spaceship is moving away from an observer at relativistic speed.Its length at rest is 100 m,but the observer measures its length as 67 m.A time interval of 100 s on the spaceship would be measured by the observer to be which of the following?
A) 200 s
B) 150 s
C) 50 s
D) 100 s

Question

Quizplus · Accepted Answer

This problem can be solved using the formula for length contraction and time dilation.

Length contraction:

L' = L*(1 - v^2/c^2)^(-1/2)

where L is the length at rest, v is the velocity, c is the speed of light, and L' is the length as measured by the observer.

Substituting the given values, we get:

67 = 100*(1 - v^2/c^2)^(-1/2)

Solving for v/c, we get:

v/c = (1 - (67/100)^2)^(1/2) = 0.8

Time dilation:

t' = t*(1 - v^2/c^2)^(1/2)

where t is the time interval on the spaceship and t' is the time interval as measured by the observer.

Substituting the given values and the value of v/c that we just calculated, we get:

t' = 100*(1 - 0.8^2)^(1/2) = 60 s

Therefore, the best choice is B) 150 s.

A Spaceship Is Moving Away from an Observer at Relativistic