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 2.0 km and a mass of 1.4×1013 kg hits the earth with an impact speed of 3.6×104 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.) Use the astronomical data

B)What percentage is this of the earth's speed around the sun?

Explanation / Answer

here,

mass of asteroid , ma = 1.4 * 10^13 kg

impact speed , vi = 3.6 * 10^4 m/s

mass of earth , me = 5.98 * 10^24 kg

a)

let the recoil's speed be v

using conservation of momentum

ma*vi = ( ma + me ) * v

1.4 * 10^13 * 3.6 * 10^4 = ( 5.98 * 10^24 + 1.4 * 10^13) * v

v = 8.43 * 10^-8 m/s

the earth recoil speed is 8.43 * 10^-8 m/s

b)

earth speed around the sun , v' = 30 km/s = 30 * 10^3 m/s

the percentage = 8.43 * 10^-8 * 100 /( 30 * 10^3)

percentage = 2.81 * 10^-10 %

the percentage is this of the earth's speed around the sun is 2.81 * 10^-10 %

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