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 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 952kg metal sphere into the asteroid at 430m/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 and it goes clean throught the asteroid and imbeds itself in a second asteroid at 3.4 x 10^9m away. initially both asteroids are stationary but after passing through the first asteroid the projectile is traveling at 150m/s and the first asteroid is traveling at 17.7707m/s. the projectile comes to a stop in a second asteroid and the second asteroid ends up with a speed of 10.2 m/s.

what is the mass of the first asteroid? (in kg)

What is the mass of the second asteroid? (in kg)

Explanation / Answer

By conservation of momentum...

For the first asteroid

mv = mv + mv

952(430) = m(17.7707) + (952)(150)

m = 15000 kg

For the second asteroid

mv = (m + m)v

(952)(150) = (m + 952)(10.2)

m = 13048 kg

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