Question

A spacecraft has a rest length of 100.0m. It passes over an antenna on a lab measurement station. According to the clock in the lab it took 0.2 s for the spacecraft to pass over the lab.

[a] How fast was the spacecraft moving with respect to the lab?

[b] How long was the spacecraft according to the observer in the lab?

[c] How long did it take the spacecraft to pass over the lab according to the clock in the spacecraft?

Answer 1

ARE YOU THE TIME IS 0.2 SECONDS ?????? BECAUSE IT IS TOO LARGE FOR A RELATIVITY QUESTION

ARE YOU THE TIME IS 0.2 SECONDS ?????? BECAUSE IT IS TOO LARGE FOR A RELATIVITY QUESTION

I THINK IT SHOULD BE MICRO SECONDS

I HAVE SOLVED THE PROBLEM WITH MICROSECONDS

PLEASE LET ME KNOW IF YOU HAVE ANY DOUBT AND LET ME KNOW IF YOU WANT TO SOLVE WITH T = 2 SECONDS

(A) Here 100 m is proper length as per lab observer at rest

so,

100 = (v / sqrt (1 - v² / c²)) * t

t = 0.2 us = 2e-7 sec

sqrt (1 - v² / c²) = v * 2e-9

squaring both sides

1 - v² / c² = v² * 2e-9²

put c = 3e8

1 - 1.11e-17v² = 4e-18v²

1 = 1.51e-17v²

solve for v, we get

v = 2.57e8 m/s

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(B) L = vt

L = 2.57e8 * 0.2e-6

L = 51.468 m

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(C) t = * time taken in lab

t = 1.938 * 0.2e-6

t = 0.388 us