Problem 9.57 Most geologists believe that the dinosaurs became extinct 65 millio

Question

Problem 9.57 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 kin and a mass of 1.0x10^13 kg hits the earth with an impact speed of 3.0x10^4 . Part A 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.) Express your answer to two significant figures and include the appropriate units. vrecoil = Value Units Part B My Answers Give Up 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 in. Express your answer using two significant figures.

Explanation / Answer

apply the law of conservation of momentum

as m1u1 + m2u2   = m1v1   m2v2

here u2 = 0   and   v1 = v2   =

V = ( 1 e 13 * 3e 4) + 0 /(1 e 13 + 5.98 e 24)

V recoil   = 5.01 e -8 m/s

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Vo around sun   = Vo^2 = GM/R

where G is 6.67 e-11

m is mass of sun = 1.99 d 30 kgs

R is Distance between Sun and the earth   = 1.49 e 11m

so

Vo^2 = 6.67 e -11 * 1.99 e 30/(1.49 e 11)

Vo = 2.98 e4 m/s

ratio o f Speeds = 5.01 e-8/(2.98 e4)

= 1.68 e -12

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