- #1

Kyliticus

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- 0

## Homework Statement

A spherical asteroid of mass m0 and radius, R, initially moving at speed v0, encounters a stationary cloud of dust. As the asteroid moves through the cloud, it collects all the dust that it hits, and slows down as a result. Ignore the increase in radius of the asteroid, and its gravitational effect on distant dust grains. Assume a uniform average density D (mass per volume) in the dust cloud. By considering momentum conservation over an infinitesimal time interval dt, show that the velocity v of the asteroid obeys a = -k*v^3, and evaluate constant k. Also, find the velocity of the asteroid as a function of time.

## Homework Equations

a = -k*v^3 (must evaluate for k)

## The Attempt at a Solution

I am at a complete loss for this question. I recall in class we did an example with a rocket and its fuel, where the rocket loss mass as the fuel it had expelled gained mass. I know this question deals with some of the same concepts, but I really need a push to get in the right direction. Thanks!