Most geologists believe that the dinosaurs became extinct 65 million years ago when a large comet or asteroid struck the earth, throwing up so much dust that the sun was blocked out for a period of many months. Suppose an asteroid with a diameter of \(2.0 \mathrm{~km}\) and a mass of \(1.0 \times 10^{13} \mathrm{~kg}\) hits the earth with an impact speed of \(4.0 \times 10^{4} \mathrm{~m} / \mathrm{s}\).

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?