You are working on a project to determine the density of asteroids in order to f

Question

You are working on a project to determine the density of asteroids in order to figure out what minerals they might contain for mining. You can figure out the volume fairly easily from images of the asteroids taken from various angles. In order to determine the mass you will shoot a 642 kg metal sphere into the asteroid at 350 m/s. By measuring the movement of the asteroid and sphere you can figure out the mass of the asteroid. Unfortunately, when you fire the projectile it goes clean through the asteroid and embeds itself in a second asteroid that is 3.4 x10^9 m away. Initially both asteroids are stationary but after passing through the first asteroid the projectile is traveling at 150 m/s and the first asteroid is traveling at 7.50877192982456 m/s. The projectile comes to a stop in the second asteroid and the second asteroid ends up with a speed of 7.1865671641791 m/s.

What is the mass of the fist asteroid? in kg

What is the mass of the second astroid? in kg

Explanation / Answer

By conservation of momentum...

For the first asteroid

mv = mv + mv

642(350) = m(7.50877192982456) + (642)(150)

m = 17100 kg

For the second asteroid

mv = (m + m)v

(642)(150) = (m + 642)(7.1865671641791)

m = 12758 kg

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