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 2.5×104 m/s .

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.)

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

given

diamer=2km, m=1*10613 kg, v=2.5*1064 m/s

A)mass of earth = 5.98*10^24 kg

velocity of earth v=?

from conservation of momentum.

mass of asteroid * velocity of asteroid = (mass of earth + asteroid) * (velocity of earth + asteroid)
10^13*2.5*10^4=(10^13+ 5.98*10^24)*(v+2.5*10^4)

v=2.4*10^4 m/s

B)earth radius r2=1.5*10^11 m

radius of  asteroid r1=1km=1000 m

You know it takes 1 year to make 1 revolution around the sun. circumference of a circle = 2*pi * radius.

circumference / 1 year = speed of the Earth

1year=3.154*10^7 sec

speed of the Earth =2*3.14*1000/3.15*10^7 =1.99*10^-4 m/s

percentage is=((1.99*10^-4)/(2.4*10^4))*100=8.291*10^-7

means it is very very negligeble

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