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 1.5×1013 kg hits the earth with an impact speed of 4.0×104 m/s . A. What is the earth's recoil speed after such a collision? (Use a reference frame in which the earth was initially at rest.) Use the astronomical data inside the back cover of the textbook. B. What percentage is this of the earth's speed around the sun?

Explanation / Answer

Given: mass of asteroid (m) = 1.5*1013 Kg speed of asteroid (v) = 4*104 m/s

We have the mass of earth (M) = 5.97*1024 Kg also the speed of earth around sun (v0) = 3*104 m/s

Now in order to calculate the recoil velocity of earth we simply apply momentum conservation (remember that the collision is inelastic) i,e

m*v = (m+M)*v1   where v1 is the recoil velocity of the earth

(A) Hence v1  = 1.5*1013*4*104/(1.5*1013 + 5.97*1024) = 1.5*1013*4*104/5.97*1024 (approximately)

So v1  = 1.005*10-7  m/s

(B) v1 is (1.005*10-7/3*104)*100 = 0.000000000335 % of the earth velocity around the sun.

Best of Luck!

Related Questions

Navigate

• Browse (All)
• Browse M
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.