Question

Jane, whose mass is 53.5 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 = 108 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.) m/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 84.0 kg. m/s

Answer 1

Given m=53.5kg, D=51.0m, F=108N, L=40.0m, ?1=45°, g=9.8m/s

(a)The final angle ?2 can be found from the horizontal distance:

D = Lsin?1+Lsin?2

Solving for ?2 gives us:

?2 = asin((D/L)-sin?1) = 34.6°

The initial & final heights are given by:

h1 = L(1-cos?1) = 11.72m

h2 = L(1-cos?2) = 7.08m

By conservation of energy, initial height & speed into wind become final height:

mgh1+½mv²-FD = mgh2

Solving for v gives us:

v = ?(2g(h2-h1)+(2FD/m)) = 10.72m/s

(b)Given m=137.5kg, Assume ?1=45°

As above: ?2=34.6°, h1=11.72m, h2=7.08m

By conservation of energy, initial height & speed with wind become final height:

mgh2+½mv²+FD = mgh1

Solving for v gives us:

v = ?(2g(h1-h2)-(2FD/m)) = 3.30m/s