Question

An astronaut in a spacecraft looks out her window and observes a comet travel in the opposite direction at a relative speed of 237 m/s. The velocity of the spacecraft is 114 m/s directly away from the sun. What is the comet's velocity relative to the sun? Assume that motion away from the sun is in the positive direction.

Answer 1

The velocity of the spacecraft with respect to the Sun is
$v_s = +114 m/s$
the velocity of the comet in the reference system of the spacecraft is
$v_c' = 237 m/s$

So, the velocity of the comet in the reference system of the Sun will be
$v_c = v_c'-v_s = -237 m/s - 114 m/s=-351 m/s$
And the negative sign tells us that the comet is directed toward the Sun.

Answer 2

Answer: The relative velocity of the comet with respect to sun is '-351 m/s'.

Explanation:

Let the magnitude of the velocity of the spaceship moving away from the sun be $|v_s|=114 m/s$

Let the magnitude of the velocity of the comet moving towards the sun be $|v_c| m/s$

Assuming the direction away from the sun to be positive then :

The velocity of the space ship :$v_s=+114 m/s$

The  velocity of the comet :$-v_c$

$v_r$ = relative velocity of spaceship with respect to comet

$v_r=-237 m/s=v_s+(-v_c)=114 m/s-v_c$

$v_c=351 m/s$

Velocity of the comet.$v_c=351 m/s$

$v_R$ = Relative velocity of comet with respect to sun:

$v_R=v_s+v_c=0 m/s+(-351 m/s)=-351 m/s$

$v_s= 0 m/s$(Sun is fixed at one point)

The negative sign means that comet is moving towards the sun.The relative velocity of the comet with respect to sun is '-351 m/s'.