can some one please help me with this impulse and momentum problem; answer is 22

Question

can some one please help me with this impulse and momentum problem; answer is 22.0m i just dont know how;please show steps and picture drawings

6. Jane is in trouble, stuck on a sandbar in the middle of a river. Hungry crocodiles are approaching, so Tarzan grabs a vine of length L = 25.0 m and swings from the higher left bank of the river. He grabs Jane and together they barely are able to swing up to the lower right bank of the river. If Tarzan's and Jane's masses are 82.0 kg and 50.0 kg, respectively, and the right bank is 2.40 m lower than the left bank, what is the width of the river? L= 25.0 m hungry crocodiles

Explanation / Answer

Let initial height of Tarzen be h

velocity at bottom before catching Jane = sqrt(2gh)

Because of momentum conservation in horizontal,

velocity after catching Jane v2 = sqrt (2gh) *M/(M+m) = sqrt(2gh)*82/132

Now by energy coservation, h2 = v2^2/2g

h-2.4 = [sqrt(2*g*h)*82/132]^2/2g

2gh-4.8g = 2gh *0.3859 or 2h*(1-0.3859) = 4.8

h = 4.8/ [2*(1-0.3859)] = 3.908 m

width = 25*( sin theta1+sin theta2) where theta1 = arccos((25-3.908)/25) = 0.5667 rad

and theta2 = arccos((25-3.908+2.4)/25) = 0.3491 rad

width = 25*( sin 0.5667 rad + sin 0.3491 rad) = 22 m answer

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