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# Differential Equations Problem?

An object with mass 121.5 kg is given an initial downward velocity −2 m/s in a medium that exerts a resistive force with magnitude proportional to the square of the speed. The resistance is 240 N when the velocity is −4 m/s. Use g =10 m/s^2

1) Write out a differential equation in terms of the velocity v, and acceleration a

2) Find the velocity v(t) for the object

I am having trouble figuring out where to start.

### 1 Answer

- rotchmLv 77 months agoFavorite Answer
Hints:

F = ma = mh'' where h is the height, or its vertical position. Wlog we will take h=0 for the init position and positive upwards. Hence initial velocity = -2 [I will be using standard units].You are also told thatF_resis = k/v². what sight will you attribute to k?And from 240 = k/(-4)², you have the magnitude of k. Thus, F = mh'' = Fg + Fr = mh''. Use the correct signs for the LHS terms. Fg is a constant [which one?]. Note that h' = v, thus Fg + Fr = mv'. This would be your DE (separable) in its "simplest" form. Surely you can take it from there.