A spaceship from another galaxy passes over the solar system directly above a radial line from the sun to the Earth. (We measure that distance to be 1.5 *1011 m.) On Earth, the spaceship is observed to be travelling at a speed of 0.80 c, for which $\gamma$ = 5/3. As measured on Earth it takes the spaceship 625 seconds to travel from the sun to Earth. When a scientist in the spaceship measures the Earth-sun distance and the time it takes her to travel that distance, she finds the results are respectively:
A)9.0* 1010 m; 375 s.
B)9.0 *1010 m; 625 s.
C)1.5 * 1011 m; 625 s.
D)2.5 * 1011 m; 625 s.
E)2.5 * 1011 m; 1042 s.

Question

Quizplus · Accepted Answer

Let's use the time dilation formula to find the time elapsed on the spaceship: 
$$\Delta t' = \frac{\Delta t}{\sqrt{1 - \frac{v^2}{c^2}}}=\frac{625}{\sqrt{1-(0.80c)^2/c^2}}\approx 375	ext{ s}$$
Next, we need to use length contraction to find the distance between the Sun and Earth as measured by the person in the spaceship:
$$L' = L\sqrt{1-\frac{v^2}{c^2}} = 1.5	imes 10^{11}\sqrt{1-(0.80c)^2/c^2}\approx 9.0	imes 10^{10}	ext{ m}$$
Therefore, the correct answer is (A).

A Spaceship from Another Galaxy Passes Over the Solar System γ\gammaγ

A Spaceship from Another Galaxy Passes Over the Solar System $\gamma$