Question

As you pilot your space utility vehicle at a constant speed toward the moon, a race pilot flies past you in her spaceracer at a constant speed of 0.780 c ,relative to you. At the instant the spaceracer passes you, both of you start timers at zero.

Part A

At the instant when you measure that the spaceracer has traveled 1.24×108m past you, what does the race pilot read on her timer?

Part B

When the race pilot reads the value calculated in the previous part on her timer, what does she measure to be your distance from her?

Answer 1

Part A)

This problem involves measurements made from two inertial refrerence frames, one attached to you and other attached to race pilot.

Distance measured by you, = proper distance, = 1.24 x 10⁸ m

Distance measure by race pilot = contracted length

Time measured by race pilot frame = proper time, since only one clock is required by race pilot

relative velocity between two frames v = 0.780 c

For frame attached to race pilot

  

Also , we know that

where

  

  

for relativity we use c = 299792458 m/s

Part B)

Again from the frame attached to race pilot

m

She measures contracted length