Chapter 2.3, Problem 26P

A rocket sled having an initial speed of $160$ mi/h is slowed by a channel of water. Assume that, during the braking process, the acceleration $a$ is given by $a(v)=-\mu v^2$, where $v$ is the velocity and $\mu$ is a constant.

As in Example $4$ in the text, use the relation $dv/dt=v\left(dv/dx\right)$ to write the equation of motion in terms of $v$ and $x$.

If it requires a distance of $2200$ ft. to slow the sled to $16$ mi/h, determine the value of $\mu$.

Find the time $\tau$ required to slow the sled to $16$ mi/h.