••• IP The starships Picard and La Forge are traveling in the same direction toward the Andromeda galaxy. The Picard moves with a speed of 0.90c relative to the La Forge. A person on the La Forge measures the length of the two ships and finds the same value, (a) Tf a person on the Picard also measures the lengths of the two ships, which of the following is observed : (i) the Picard is longer; (ii) the La Forge is longer; or (iii) both ships have the same length? Explain, (b) Calculate the ratio of the proper length of the Picard to the proper length of the La Forge.
Solution 35 P:
Step 1 of 2:-
Here, we have to find which of the ships is longer or shorter or both are of same length with respect to picard’s frame of reference.
The speed of picard wrt la forge is 0.90 c.
The person in la forge, measures the length of both the ships. As he is at the rest frame of la forge, he will measure the proper length of la forge and the contracted length of picard.
Both have the same length in la forge’s frame. But he is measuring the contracted length of picard.
But, picard will measure that la forge is moving in the opposite direction with a speed of 0.9 c.
Picard’s proper length is already greater than la forge, and again the person on picard is measuring the contracted length of la forge.
So, the person in picard will observe that (i) the Picard is longer.