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 .

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.)

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. (vrecoil/vorbital)

Explanation / Answer

using law of conservation of momentum

momentum before collision = momentum after collision

(2.5*10^14*3.5*10^4) = 5.98*10^24*v

v = 1.46*10^-6 m/sec

vrecoil = 1.46*10^-6 sec

vorbital = 30000 m/sec

required percentage is ((1.46*10^-6)/30000)*100 = 4.86*10^-9 %

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