Having aced your introductory physics course, you are hired as a summer intern a

Question

Having aced your introductory physics course, you are hired as a summer intern at NASA. You are sent as part of a team to explore the possibility of mining iron from a small, airless spherical asteroid with a radius of 474 km and a surface acceleration of 2.9 m/sec2.

Mass of asteroid = 9.768*10^21 kg

How far will the 3 kg rock go if it leaves the asteroids surface with a vertical velocity of 1000 m/sec?";

What will the speed of the 6 kg rock be at the surface of the asteroid if it is dropped from a point 1000km above the surface of the asteroid?

Explanation / Answer

How far will the 3 kg rock go if it leaves the asteroids surface with a vertical velocity of 1000 m/sec?"

vf^2 = vi^2 + 2 * a * d, vf = 0, vi = 1000, a = -2.9
0 = 1000^2 + 2 * -2.9 * d
d = 1000^2/ 5.8
This is approximately 1.724 * 10^5 meters

OR

H = (.5 * V^(2) * R^(2)) / (GM - .5 * V^(2) * R)

hmax = 10^6/5,800 = 172 km approx.

What will the speed of the 6 kg rock be at the surface of the asteroid if it is dropped from a point 1000km above the surface of the asteroid

vf^2 = vi^2 + 2 * a * d, vi = 0 a= 2.9, d = 1 * 10^6
vf^2 = 2 * 2.9 * 1 * 10^6
vf = 5.8 * 10^6
This is approximately 2408 m/s.

OR

V = sqrt( (GMH) / ( (.5 * R^(2)) + (.5 * RH)))
V = 5.8*10^6 = 10^3*5.8 = 10^3*2.41 m/sec

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