Question

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Answer 1

dF = dP/dT

where F = mg, and P = mv

Mg = d(MV)/ dT = M dV/ d t + V dM/ d t

since  

dM/ d t = kMV

kV2 + dV/d t = g

Then we can see, as the drop falls, it’s velocity increases due to gravity. However, there

is a limit for this velocity because as the drop speeds up, its acceleration decreases rapidly

and will become negligible as the time goes to infinity. So the speed of the drop will

eventually become constant.

To compute the terminal constant speed, we could set dV/d t = 0

 

then we have  

k Vt2 = g

Vt = √(g/k)

Hope this helps you

Answer 2

Answer:

Explanation:

dF = dP/dT

where F = mg, and P = mv

Mg = d(MV)/ dT = M dV/ d t + V dM/ d t

since

dM/ d t = kMV

kV2 + dV/d t = g