Spaceship A traveling past us at 07c sends a message capsule

Spaceship A traveling past us at 0.7c, sends a message capsule to spaceship B which is in front of A and is traveling in the same direction as A at 0.8c relative to us. The capsule travels at 0.95c relative to us. A clock that measures the proper time between the sending and receiving of the capsule travels:

a. in same direction as spaceships at 0.7c relative to us.
b. in opposite direction from the spaceships at 0.7c relative to us.
c. in same direction as spaceships at 0.8c relative to us.
d. in same direction as the spaceships at 0.95c relative to us.
e. in opposite direction from the spaceships at 0.95c relative to us.

Please expalin how you arrived at the right answer.

Solution

Ans

Proper time is defined as the time measured by a clock following the time-like world line.

It is a Lorentz scalar and independent of coordinates.\'

In other words,proper time can only be measyured in the same inertial frame.According to the principles of special theory of relativity, easurement of time from any other inertial frame will always be greater.

Hence, in this case, to measure proper time, the clock has to travel in the same intertial frame i.e 0.95 C

in the same direction of the spaceships relative to us.

Hence the correct option is D