Ballistics tests often involve shooting a bullet into a \"soft\" viscous materia

Question

Ballistics tests often involve shooting a bullet into a "soft" viscous material to stop the slug without damaging it. Consider shooting a bullet of mass ?? into 1) a medium whose resistance is proportional to the speed, 2) a medium whose resistance is proportional to ??^3/2, and 3) a medium whose resistance is proportional to ??^2. Assume in all cases both the initial speed of the bullet (??0) and the constant of proportionality (??) are the same. In each case, compute the time the bullet travels before slowing to a velocity of 10^?4 ??0. In all cases the bullet is shot horizontally into the medium and the gravitational force can be neglected.

Explanation / Answer

This question is truly a pain in the ass. I think I'll be able to approach this later tonight and will post the answer. Our textbook doesn't help with the addtion of 10^-4 v0 to this problem

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