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

5.0km and a mass of 2.5?1014kg hits the earth with an impact speed of 4.0?104m/s .

Part A

What is the earth's recoil speed after such a collision? Assume that the mass of the earth is 5.98?1024 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.

Part 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?1011 m.

Express your answer using two significant figures.

Explanation / Answer

Given

Diameter of the steroid Da = 5.0 x 103 m

Mass of the asteroid ma = 2.5 x 1014 kg

Initial velocity of the asteroid va = 4.0 x 104 m/s

Initial velocity of earth ve = 0 m/s

radius of earth’s orbit r = 1.5 x 1011 m

Known

Mass of the earth me = 5.97 x 1024 kg

Solution

Part A

When the asteroid collides with the earth it is fused to the earth and they move together with the same final speed.

This is an inelastic collision. As per the law of conservation of momentum

Momentum before collision = Momentum after the collision

mava + meve = (ma + me) vrecoil

since ve = 0

mava = (ma + me) vrecoil

vrecoil = mava/ (ma + me)

vrecoil = 2.5 x 1014 x 4.0 x 104 / (2.5 x 1014 +5.97 x 1024)

vrecoil = 1.68 x 10-6 m/s

Part B

Total length of earth’s orbit is

S = 2r

S = 2 x 3.14 x 1.5 x 1011

S = 9.42 x 1011 m

Earth crosses this length in one year

Vorbital = 9.42 x 1011 m/year

Vorbital = 9.42 x 1011 / 365.25 x 24 x 60 x 60

vorbital = 2.98 x 104 m/s

vrecoil/vorbital = 1.68 x 10-6/2.98 x 104

vrecoil/vorbital = 0.564 x 10-10

vrecoil/vorbital = [0.564 x 10-10 x 100 ] %

vrecoil/vorbital =5.64 x 10-9 %

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