A spaceship enters the solar system moving toward the Sun at a constant speed relative to the Sun. By its own clock, the time elapsed between the time it crosses the orbit of Jupiter and the time it crosses the orbit of Mars is $50.0$ minutes. How fast is the spaceship traveling towards the Sun? The radius of the orbit of Jupiter is $778 \times 10 ^ { 9 } \mathrm {~m}$, and that of the orbit of Mars is $228 \times 10 ^ { 9 } \mathrm {~m}$.
A) $0.522 c$
B) $0.982 c$
C) $0.438 c$
D) $0.319 c$
E) $0.671 c$

Question

Quizplus · Accepted Answer

The spaceship's speed can be calculated using the distance covered and the time taken. The distance between the orbits of Jupiter and Mars is the difference in their radii, $778 \times 10^9 \, \text{m} - 228 \times 10^9 \, \text{m} = 550 \times 10^9 \, \text{m}$. Given the time is 50.0 minutes, which is $50 \times 60 = 3000 \, \text{seconds}$, the speed $v$ is distance/time = $550 \times 10^9 \, \text{m} / 3000 \, \text{s}$. To find the fraction of the speed of light $c$, we divide by $c = 3.00 \times 10^8 \, \text{m/s}$, resulting in $v/c \approx 0.522$, making the correct answer $0.522 c$.

A Spaceship Enters the Solar System Moving Toward the Sun 50.050.050.0

A Spaceship Enters the Solar System Moving Toward the Sun $50.0$