Please show all work and all formulas used I am really trying to learn Q3: Space

Question

Please show all work and all formulas used I am really trying to learn

Q3: Space pilot Jim measures the length of his space ship to be 2450 m. The ship drifts at a constant velocity of 0.740c past a space platform from which Mary (at rest on the platform) observes its passage. (a) What is the length of the space ship according to Mary? (b) According to Mary, what is the time interval between the bow (front) of the ship passing her and the stern (rear of the ship passing her? (c) According to Jim, what is the time interval between the bow (front of the ship passing Mary and the stern (rear of the ship passing her?

Explanation / Answer

a) Observed length according to Mary:

L0= Lr(1-v2/c2)1/2 = 2450(1-(0.74c)2/c2)1/2 = 2450*0.672 = 1647.886 m

b) Observed time can be stated as: t0 = tr/(1-v2/c2)1/2

t0 is 0.740, tr is 1

1/0.7402 = 1-v2/c2 = 1.826

v = (0.826c2)1/2 = 0.908c m/s

So according to Mary, time interval between the bow(front) of the ship passing her and the stern(rear) of the ship passing her is 1647.886/0.908c = 604.95*10-8 s

c) So according to Jim, time interval between the bow(front) of the ship passing Mary and the stern(rear) of the ship passing her is 2450/0.908c = 899.41*10-8 s

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