1 out of 5 attempts NASA has taken an increased interest in near Earth asteroids

Question

1 out of 5 attempts NASA has taken an increased interest in near Earth asteroids. These objects, popularized in recent blockbuster movies, can pass very close to Earth on a cosmic scale, sometimes as close as 1 million miles. Most are small less than 500 m across -and while an impact with one of the smaller ones could be dangerous, experts believe that it may not be catastrophic to the human race. One possible defense system against near Earth asteroids involves hi incoming asteroid with a rocket to divert its course. Assume a relatively small asteroid with a mass of 1.71 1010 kg is traveling toward the Earth at a modest speed of 13.8 km/s. Part 1 out of 2 a) How fast would a large rocket with a mass of 90,000. kg have to be moving when it hit the asteroid head on in order to stop the asteroid? VR? tting an - 10 m/s next

Explanation / Answer

asteroid problem :

M = mass of asteroid = 1.71 x 1010 kg

V = velocity of asteroid = 13.8 km/s = 13800 m/s

m = mass of rocket = 90,000 kg

v = velocity of rocket = ?

Using conservation of momentum

initial total momentum = final total momentum

MV - m v = 0

(1.71 x 1010) (13800) - (90000) v = 0

v = 2.6 x 109 m/s

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