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 2.0km and a mass of 1.0x10^13kg hits the earth with an impact speed of 2.5x10^4m/s .

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.

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 1.5?10^11 m.

Express your answer using two significant figures.

Explanation / Answer

A]

Applying law of conservation of momentum

masteroidUasteroid+mearth*Uearth= masteroid Vasteroid+mearth* Vearth

Vearth=[mearth -masteroid ]Uearth/[mearth +masteroid]+[2*masteroid *Uasteroid ]/[mearth +masteroid ]
Pligging the values, we get

Vearth= 0+[2*masteroid *Uasteroid ]/[mearth +masteroid ]

        =2*1.0x1013kg *2.5x104m/s/[5.98?1024 kg+1.0x1013kg]  

       =8.36*10-8m/s

Earth's recoil speed after such a collision is 8.36*10-8m/s

B)

Here gravitational force between earth and sun balances the centripetal force of earth

FG= FC

GMm/r2= mv2/r                  [m-mass of earth, M- mass of sun=2*1030 kg]

v=[GM/r]1/2

v=[6.67*10-11*2*1030 /1.5*1011 ]1/2 =2.98*104 m/s

Vrecoil/Vorbit=8.36*10-8m/s/2.98*104 m/s= 2.8*10-12

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