A fellow astronaut passes by you in a spacecraft traveling at a high speed. The astronaut tells you that his craft is 21.1 m long and that the identical craft you are sitting in is 17.3 m long. (a) According to your observation, how long is your craft? m (b) According to your observation, how long is the astronaut's craft? m (c) According to your observation, what is the speed of the astronaut's craft relative to your craft?

A) 21.1 m

B) 17.3 m

C) 3.267x10^7 m/s

Explanation:

This is a case of special relativity.

Let the relative speed of astronauts ship to my ship be v.

According to my observation,

My craft is 21.1 m long, according to my observation, astronauts craft is 17.3 m long.

If we fix the reference frame as my ship, then the rest lenght of our identical crafts is 21.1 m and the relativistic lenght is 17.3 m

l' = 21.1 m

l = 17.3 m

From l = l' (1 - p^2) ^0.5

Where p is c/v, and c is the speed of light

17.3 = 21.1 x (1 - p^2) ^0.5

0.82 = (1 - p^2) ^0.5

Square both sides

0.67 = 1 - p^2

P^2 = 0.33

P = 0.1089

Revall p = v/c

v/c = 0.1089

But c = speed of light = 3x10^8 m/s

Therefore,

v = 3x10^8 x 0.1089 = 3.267x10^7 m/s