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 510 m/srelative 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 510 m/srelative 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

m = mass of asteroid = 5 x 109 kg

vi = initial velocity at distance = 510 m/s

vf = final velocity just before hitting = ?

M = mass of earth = 5.98 x 1024 kg

ri = initial distance between asteroid and earth = 6 x 109 m

rf = final distance between asteroid and earth = 6.37 x 106 m

using conservation of energy

initial KE + initial GPE = final KE + final GPE

(0.5) m vi2 - GMm/ri = (0.5) m vf2 - GMm/vf

(0.5) vi2 - GM/ri = (0.5) vf2 - GM/vf

(0.5) (510)2 - (6.67 x 10-11) (5.98 x 1024)/(6 x 109) = (0.5) vf2 - (6.67 x 10-11) (5.98 x 1024)/(6.37 x 106)

vf = 11185 m/s = 1.1 x 104 m/s

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