Jane, whose mass is 46.0 kg, needs to swing across a river (having width D ) fil

Question

Jane, whose mass is 46.0 kg, needs to swing across a river (having width D) filled with person-eating crocodiles to save Tarzan from danger. She must swing into a wind exerting constant horizontal force F, on a vine having length L and initially making an angle ? with the vertical (see below figure). Take D = 51.0 m, F= 110 N, L = 40.0 m, and ? = 45.0°.

(a) With what minimum speed must Jane begin her swing to just make it to the other side? (If Jane can make it across with zero initial velocity, enter 0.)  

ANSWER 15.62m/s

(b) Once the rescue is complete, Tarzan and Jane must swing back together across the river. With what minimum speed must they begin their swing? Assume that Tarzan has a mass of 72.0 kg.

ANSWER: ???

For part b) the answer is NOT 9.75m/s nor 28m/s... I posted the same question already twice and tutors got me two different WRONG answers. Please. Is there anyone who can help me solve this problem CORRECTLY?

Explanation / Answer

here,

mass of jane = M = 46 kg
Width of river = D = 51 m
Forec due to Wind = F = 110N
Length of wine = L = 40m
Initial Angle = 1 = 45.0°

A)

First, Solving for Final Angle = 2 or Fi

D = L*Sin1 + L*Sin2

2 = arcSin((D/L)-sin1)
= arcSin((51/40)-sin45)
= 34.6°

Intial Height = h1 = L(1-cos1) = 40(1- cos45) = 11.71 m
Final Height = h2 = L(1-cos2) = 40(1- cos34.6) = 7.07 m

Therefore

PE1 = mgh1 = 46*9.8*11.71 = 5278.86 J
PE2 = mgh2 = 46*9.8*7.07 = 3187.15 J

KE = 0.5 * m * V^2
KE = 0.5 * 46 * V^2
KE = 23*V^2

Work done by air = F*D = 110*51 = 5610 N

From Conservatin of Energy,

PE1 + KE -FD = PE2
5278.86 + 23*V^2 - 5610 = 3187.15
V = 12.36 m/s

The Velocity of jane will be 12.36 m/s

Part B:

PE1 = mgh1 = (46+72)*9.8*11.71 = 13541.44 J
PE2 = mgh2 = (46+72)*9.8*7.07 = 5175.74 J

KE = 0.5 * m * V^2
KE = 0.5 * (46+72) * V^2
KE = 59*V^2

Work done by air = F*D = 110*51 = 5610 N

From Conservatin of Energy,

PE2 + Ke + F*D = PE1

5175.74 + 59*V^2 + 5610 = 13541.44

V = 6.83 m/s

Tarzan and Jane must swing back together at 6.83 m/s

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