Question

at what speed $v_2$ will the crewman hit the bottom of the ravine? assume no air resistance.

Explanation:

Step1: Identify relevant kinematic equation

We use $v^{2}=v_{0}^{2}+2gh$ where initial vertical - velocity $v_{0}$ (assuming free - fall from rest vertically) is 0, $g = 9.8\ m/s^{2}$ is acceleration due to gravity and $h$ is the height of the fall.

Step2: Rearrange and solve

If $v_{0}=0$, the equation simplifies to $v=\sqrt{2gh}$. We need the height of the ravine. Since it's not given in the problem statement, we can't calculate a numerical value. But if we assume a height $h$ was given previously, we would substitute it into the formula. For example, if $h = 12\ m$, then $v=\sqrt{2\times9.8\times12}=\sqrt{235.2}\approx15.33\ m/s$. However, without the height value, we can only state the general formula.

Answer:

The general formula for the speed $v$ is $v=\sqrt{2gh}$ where $g = 9.8\ m/s^{2}$ and $h$ is the height of the fall.