What Minimum Speed Must Jane Have to Swing Across the River?

AI Thread Summary
To determine the minimum speed Vernie must have to swing across the river, the problem requires calculating the potential energy (PE) and kinetic energy (KE) involved in the swing. Given the mass of Vernie and Charlie, the width of the river, the wind force, and the angle of the vine, the equations PE = mgh and KE = 1/2mv² are utilized. The initial calculations suggest that Vernie needs to achieve a specific speed to counteract the wind and reach the other side. Additionally, once the rescue is complete, the combined mass of Vernie and Charlie will affect the minimum speed needed for their return swing. The discussion emphasizes the importance of energy conservation in solving the problem.
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Homework Statement


Vernie, whose mass is 45.0 kg, needs to swing across a river filled with crocodiles in order to rescue Charlie,whose mass is 75.0 kg. However, she must swing into a constant horizontal wind force on a vine that is
initially at an angle of θ with the vertical. The width of the river between them is D = 60.0 m, F = 120 N, Length of

the rope L = 45.0 m, and θ = 60.0°.
(a) With what minimum speed must Jane begin her swing in order to just make it to the other side?
(b) Once the rescue is complete, Vernie and Charlie must swing back across the river. With what minimum

speed must they begin their swing?



Homework Equations


L=L-(Lcosθ)
KE = 1/2mv2
PE = mgh.


The Attempt at a Solution


PE = KE
mgh = 1/2mv2
 
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