A NASA satellite has just observed an asteroid that is on a collision course wit

Question

A NASA satellite has just observed an asteroid that is on a collision course with the Earth. The asteroid has an estimated mass, based on its size, of 5×109kg. It is approaching the Earth on a head-on course with a velocity of 860 m/s relative to the Earth and is now 6.0×106 km away.

Part A

With what speed will it hit the Earth's surface, neglecting friction with the atmosphere?

Express your answer using two significant figures.

A NASA satellite has just observed an asteroid that is on a collision course with the Earth. The asteroid has an estimated mass, based on its size, of 5×109kg. It is approaching the Earth on a head-on course with a velocity of 860 m/s relative to the Earth and is now 6.0×106 km away.

Part A

With what speed will it hit the Earth's surface, neglecting friction with the atmosphere?

Express your answer using two significant figures.

Explanation / Answer

Given,

m = 5 x 109 kg ; v1 = 860 m/s ; r1 = 6 x 106 km = 6 x 109 m

The collision will happen at r2 = radius of earth = 6.37 x 106 m

Let v2 be the speed with which it collides.

We know from energy conservation:

KEi + Ui = KEf + Uf

KEf = KEi - Uf + Ui

1/2 m v22 = 1/2 m v12 - (- GMm/r2) + (-GMm/r1)

On simplifying and solving for v2 we get:

v2 = sqrt [ v12 + 2 GM(1/r2 - 1/r1)]

v2 = sqrt [ 860 x 860 + 2 x 6.67 x 10^-11 x 6 x 10^24 (1/ 6.37 x 10^6 m - 1/ 4 x 10^9 m) ]

v2 = 1.12 x 10^4 m/s

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