Chapter 2.3, Problem 30P

A mass of $0.40$ kg is dropped from rest in a medium offering a resistance of $0.2\left|v\right|$, where $v$ is measured in metersper second.

If the mass is dropped from a height of $25$ m, find its velocity when it hits the ground.

If the mass is to attain a velocity of no more than $8$ m/s, find the maximum height from which it can be dropped.

Suppose that the resistive force is $k\left|v\right|$, where $v$ is measured in meters per second and $k$ is a constant. If the mass is dropped from a height of $25$ m and must hit the ground with a velocity of no more than $8$ m/s, determine the coefficient of resistance $k$ that is required.