A spaceship flies past an experimenter who measures its length to be three quart

Question

A spaceship flies past an experimenter who measures its length to be three quarters the length he had measured when the spaceship was at rest. An astronaut aboard the spaceship notes that his clock ticks at 1-second intervals. What is the time between ticks as measured by the experimenter?

Part A What is the time between ticks as measured by the experimenter? Espress your answer o wo signlfceant lgures and include the appropiriate units At-4.1 Submit My Answers Give Up Incorrect; Try Again; 2 attempts remaining

Explanation / Answer

We will solve it step by step

This is a problem of special relativity, we write the expressions for time and length

L = Lp /

t = tp

= 1/ sqrt (1- (v/c)2 )

Where

p refers to the values measured in the system where the object does not move

Data

L = ¾ Lp

tp = 1 s

We calculate the speed of the ship

L = Lp /

¾ Lp = Lp sqrt (1-(v/c)2 )

(¾ )2 = 1 – (v/c)2

(v/c)2 = 1 – 9/16

v/c = sqrt 0.4375

v = c 0.661

Given the speed of the ship, we calculate the time dilation

t = 1 1/sqrt( 1 - ( 0.661c/c)2 )

t =1 / sqrt ( 1- 0.4369) = 1/ sqrt (0.5631)

t = 1.33 s

This is the time measured by the experimenter who sees move the ship

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