Acomet is traveling through space with speed 3.01 ✕ 104 m/s when it encounters an asteroid that was at rest. the comet and the asteroid stick together, becoming a single object with a single velocity. if the mass of the comet is 1.71 ✕ 1014 kg and the mass of the asteroid is 6.06 ✕ 1020 kg, what is the final velocity of their combination? (assume the comet's initial direction is positive. indicate the direction with the sign of your answer.)

Explanation:

According to the conservation of linear momentum principle, the initial momentum (before the collision) must be equal to the final momentum (after the collision):

(1)

In addition, the initial momentum is:

(2)

Where:

is the mass of the comet

is the mass of the asteroid

is the velocity of the comet, which is positive

is the velocity of the asteroid, since it is at rest

And the final momentum is:

(3)

Where:

is the final velocity

Then :

(4)

Isolating :

(5)

Finally:

This is the final velocity, which is also in the positive direction.