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 1.0×1013 kg hits the earth with an impact speed of 4.5×104 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.) Express your answer to two significant figures and include the appropriate units.

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. Express your answer using two significant figures.

Explanation / Answer

as per conservation of momentum since no external forces are acting

Mv + mu = (M+m) V

M = mass of earth and v be its initial velocity which is 0

m = mass of asteroid and u be its initial velocity which is 4.5*10^4 m/s

V is the final velocity of combined earth and asteroid since it is a in elastic collision

therefore V = Mv + mu/(M+m) = 1*10^13*4.5*10^4/(1*10^13 + 5.98 * 10^24) = 7.525* 10^-8 m/s

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given radius of earth as 1.5*10^11 m

it takes 365.25 days to rotate

so speed of earth is 2*pi*1.5*10^11/[365.25*24*60*60] = 2.985 *10^4 m/s

so the ratio of recoil speed to speed of earth = 7.525* 10^-8 m/s / 2.985 *10^4 m/s = 2.52 *10^-12

the percentage is 2.52 * 10^-10 %

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