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 2.5x10^14 kg hits the earth with an impact speed of 4.0x10^4 m/s. What is the earth's recoil speed after such a collision? Assume that the mass of the earth is 5.98. 10^24 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 1.5. 10_11 m.

Explanation / Answer

(a).

P = 0

M V + m v - (M + m) v' = 0

M (0) + (2.5*10^14)(4 * 10^4) -(5.98 * 10^24 + 4 * 10^4) v' = 0

v' =1.6710^(-6) m/s


(b).
vf/ve = (1.67 * 10^-6 m/s) / (3.0 * 10^4 m/s) = 5.56*10^-11 or 5.56*10^-10%

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