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.

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

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

Answer Link

IlaMends IlaMends · Answer 2 · 2019-01-21T09:57:38+01:00

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 [tex]|v_s|=114 m/s[/tex]

Let the magnitude of the velocity of the comet moving towards the sun be [tex]|v_c| m/s[/tex]

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

The velocity of the space ship :[tex]v_s=+114 m/s[/tex]

The velocity of the comet :[tex]-v_c[/tex]

[tex]v_r[/tex] = relative velocity of spaceship with respect to comet

[tex]v_r=-237 m/s=v_s+(-v_c)=114 m/s-v_c[/tex]

[tex]v_c=351 m/s[/tex]

Velocity of the comet.[tex]v_c=351 m/s[/tex]

[tex]v_R[/tex] = Relative velocity of comet with respect to sun:

[tex]v_R=v_s+v_c=0 m/s+(-351 m/s)=-351 m/s[/tex]

[tex]v_s= 0 m/s[/tex](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'.