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 5.0 km and a mass of 2.5×1014 kg hits the earth with an impact speed of 3.5×104 m/s .

Part A What is the earth's recoil speed after such a collision? Assume that the mass of the earth is 5.981024 kg. (Use a reference frame in which the earth was initially at rest.)

Part B 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 1.51011 m.

Explanation / Answer

here,
mass of earth,me = 5.972 * 10^24 kg
mass of asteroid, ma = 2.5 * 10^14 kg
velocity of asteroid, va = 3.5 * 10^4 m/s

from conservatin of momentum : initial = final
me*ve + ma*va = (me+ma)*V

solving for recoil velocity after collision, V

V = (ma*va)/(me+ma)
V = (2.5 * 10^14 * 3.5 * 10^4 ) / (5.972 * 10^24 + 2.5 * 10^14 )
V = 1.465*10^-6 m/s

PART B:
Average earth's orbital speed, Ve = 30 km/s

% = V/Ve
% = (1.465*10^-6) /( 3 *10^4)
% = 4.9*10^-9 or 5*10^-9
which is very tiny

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