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 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

we will use conservation of momentum,

V ( M+m) = mU

V = mU/ ( M+m)= (2.5×10^14) (2.5×10^4) /( 2.5 x 10^14+ 5.98 x 10^24) =1.045 x 10^-6 m/s

b) v ( speed aroound sun) = 2pir/ T = ( 2x 3.14x 1.5 x 10^11) / (365 x 24x 3600) = 2.987 x 10^4 m/s

1.045 x 10^-6 / ( 3x 10^4) x100 =0.348 x 10^ -8 % or 3.48 x 10^-7 %

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