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 1.0×10^13 kg hits the earth with an impact speed of 2.5×10^4 m/s .

A) What is the earth's recoil speed after such a collision? Assume that the mass of the earth is 5.981024 kg.

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 1.51011 m.

I need help with these problems please! I could benefit from the whole step by step not just the answers please. Thanks. :)

Explanation / Answer

Given :-

a) Mass = 1,0* 10^13kg, speed = 2.5 * 10^4 m/s,

momentum = mass*speed

1.0 * 10^13kg * 2.5 * 10^4 m/s = 2.5×10^17 kg m/s

Assuming all that momentum was transferred to the Earth.

Assuming mass of earth = 5.98 × 10^24 kilograms

Assuming initial velicity of earth is zero m/s as given

New momentum of earth is 2,5×10^17 kg m/s

So what is the new speed of the earth?

2,5×10^17 kg m/s = 5.98 × 10^24 kg * speed

= 0.41×10^-7 m/s
So the asteroid's impact on the earth's velocity was negligible.

b)First we need to calculate earth's orbit circumfrence

As radius of orbit given=1.5 * 10^11m

circumfrenec=2 * pi * r

= 2 * 3.14 * 1.5 * 10^11m

=9.42 * 10^11m

Earth's speed around the sun= (circumfrence of orbit)/orbital period(365 days)

=(9.42 * 10^11)/3.16 * 10^7 m/s (no of secons in 365 days)

=2.98 * 10^4 m/s

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