question 1.14 please. In particular, I need detail explaining how to do the inte

Question

question 1.14 please.

In particular, I need detail explaining how to do the integral where you find the general equation for v as a function of time. it seems on chegg solutions there is a part where it gets into arctanh and substituting vmax in, and that is very confusing and unfamiliar for me. At one point vmax becomes vmax^2 and it looks to me like it happens out of nowhere.

thanks, and I hope you have a good day!

this is a fluid mechanics problem, and it is from it is from Fox and McDonald's 8th edition

Explanation / Answer

F=ma.....................(1)

Fd=kv^2..................(2)

Net force acting on sky diver=Fg - kV^2 ..............(3)

Equating equation (1)=(3)

Fg - kV^2 = ma

mg -.25V^2 = ma

mg - .25V^2 = 0 (a=0 because of terminal velocity)

Therefore Vmax = 52.4 m/s

To fin the speed reaches after 100m of fall-

First find V(t). Apply Newton's 2nd law again:

Fnet = ma = m dv/dt

The forces acting on the sky diver, as you noticed are: Fnet = mg - k v^2

Now you can solve this differential equation for V(t).

The position function, s(t), can then be found from: V(t) = ds(t) / dt.

Note- you have to solve this differential equation to find the speed.I do not have idea about it .Hope you can solve it and hoping my solution help you out for this problem.

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