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A spaceship travels with a speed of 0.8 c as it passes by the Earth on its way t

ID: 1397913 • Letter: A

Question

A spaceship travels with a speed of 0.8 c as it passes by the Earth on its way to a distant star, as shown in the diagram below. The pilot of the spaceship measures the length of the moving ship as 50 m.

Determine its length as measured by a person on Earth. Answer in units of m

The pilot of the spaceship observes that the spaceship travels for 7 years. Determine how much time has passed according to a person on Earth. Answer in units of years.

Some time after passing the Earth, the pilotshoots a laser pulse backward at a speed of 3 × 108 m/s with respect to the spaceship. Determine the speed of the laser pulse as measured by a person on Earth. Answer in units of m/s.

Explanation / Answer

L0 = 50 m

v = 0.8 c

Applying length contraction,

L = L0 * sqrt [1 - v2/c2]

= 50 * sqrt [1 - 0.8 c 2/c2]

= 30 m

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delta T = delta T0 / gamma

= 7 years / 0.6

= 11.67 years

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A laser pulse travels at the speed of light, independent of the frame in which it is measured ( the key point of special relativity).

Thus the Earth observer sees the pulse traveling at the same speed as the pilot

3 × 108 m/s .

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