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

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

Step-by-step 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'.

Answer 2

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.