How do I find the recoil speed after two objects collide?

Question

Suppose an asteroid with a diameter of 2.0 km and a mass of 1.40 x 10^13 kg hits the earth with an impact speed of 3.30 x 10^4 m/s.

(a) What is the earth's recoil speed after such a collision? (Use a reference frame in which the earth was initially at rest.)

(b) What percentage is this of the earth's speed around the sun? (Use 1.50 1011 m as the mean distance from the earth to the sun.)

Answer 1

use conservation of momentum

m1V1 +m2V2 = m1V3 + m2V4

conditions

if m1 or m2 are initially at rest: V1 or V2 =0

if m1 and m2 stick together after collision (inelastic):

V3 = V4

so conditions on your problem:

V1 = 0 and V3 = V4