Jane, whose mass is 50.0 kg, needs to swing across a river (having width D) fill

Question

Jane, whose mass is 50.0 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 vector F , on a vine having length L and initially making an angle with the vertical (see below figure). Take D = 47.0 m, vector F = 113 N, L = 40.0 m, and = 48.0°.

(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.)
.

(b) Once the rescue is complete, Tarzan and Jane must swing back across the river. With what minimum speed must they begin their swing? Assume that Tarzan has a mass of 80.0 kg.

Explanation / Answer

a)

here

D = L * sin(theta1 + L * sin(theta2)

then

theta 2 = sin^-1( (D / L) - sin(theta 1)

theta 2 = sin^-1( ( 47 / 40) - sin(48deg) )

theta = 25.6 deg

the initial and final heights are

h1 = L * (1 - cos(theta1) = 40 * ( 1 - cos(48deg)) = 13.2 m

h2 = L * (1 - cos(theta 2) = 40 * (1 - cos(25.6)) = 3.92 m

by conservation energy

m * g* h1 + 0.5 * m * v^2 - F * D = m * g * h2

50 * 9.8 * 13.2 + 0.5 * 50 * v^2 - 113 * 47 = 50 * 9.8 * 3.92

v= 5.52 m/s

b)

the mass is = 80 + 50 = 130 kg

then using the same formula

m * g* h1 + 0.5 * m * v^2 - F * D = m * g * h2

130 * 9.8 * 13.2 + 0.5 * 130 * v^2 - 113 * 47 = 130 * 9.8 * 3.92

v = 10 m/s

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