An observer moving toward Earth with a speed of 0.95 c notices that it takes 4.9
ID: 1492174 • Letter: A
Question
An observer moving toward Earth with a speed of 0.95c notices that it takes 4.9 min for a person to fill her car with gas. Suppose, instead, that the observer had been moving away from Earth with a speed of 0.80c.
Part A
How much time would the observer have measured for the car to be filled in this case?
Express your answer using two significant figures.
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An observer moving toward Earth with a speed of 0.95c notices that it takes 4.9 min for a person to fill her car with gas. Suppose, instead, that the observer had been moving away from Earth with a speed of 0.80c.
Part A
How much time would the observer have measured for the car to be filled in this case?
Express your answer using two significant figures.
t = minSubmitMy AnswersGive Up
Incorrect; Try Again; 4 attempts remaining
Explanation / Answer
t = first observed time (=4.9 min);
t = 2nd observed time (unknown; this is the quantity we want to find);
V = observer's initial speed (=0.95c);
V = observer's final speed (=0.80c);
Lorentz factors for V and V:
= 1/(1(V/c)²)
= 1/(1(V/c)²)
The "proper time" (the time measured by the person filling her car) is:
t = t/
The proper time is stated to be the same for both observations, so we also have:
t = t/
Combine those two equations and solve for t
t = t(/)
= t((1(V/c)²)/(1(V/c)²))
t2 = 4.9((1(0.95c/c)²)/(1(0.80c/c)²)) = 2.55 min.........Ans.