Most geologists believe that the dinosaurs became extinct 65 million years ago w

Question

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 9.0 km and a mass of 1.0×10^15 kg hits the earth with an impact speed of 3.5×104 m/s. What is the Earth's recoil speed after such a collision? Assume that the mass of the Earth is 5.98x10^24 kg. (Use a reference frame in which the Earth was initially at rest). What percentage is this of the earth's speed around the sun? Assume that the orbit of the earth is a circle with the radius of 1.510^11 m.

Explanation / Answer

use the law of conservtion of momentum here as

mv = ( M+m) V

V = mv/(m+M)

V = 1 e 15 * 3.54e 4/( 1 e 15 + 5.98 e 24)

V = 5.91 e -6 m/s

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Vorbita = Vo = 2piR/T

Vo = 2* 3.14 * 1.5 e 11/(365 * 24* 60*60)

Vo = 29.8 km/s

so % of speed = 5.91 e -6/29800 = 2 e -10

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