ane, whose mass is 46.5 kg, needs to swing across a river (having width D) fille

Question

ane, whose mass is 46.5 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 = 100 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.) (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 84.8 kg.

Explanation / Answer

Work done against the wind is,

            WW = F D

                  = (100 N)(51)

                  = 5100J

The sum of initial kinetic energy, potential energy on river bank and work done against the air is equal to the potential energy on the other river bank

Kei + Pe1 - W= Pe2

If the river banks are on the same level, then

Pe1 = Pe2

That is,

Kei = W

       0.5mV2= F D

                 V=( 2 F D /m)

                  = (2(5100 J)/ 46.5)

                 = 14.8 m/s

(b)

In this case, we need to add the Tarzns weight.

V=( 2 F D /(mJ + mT))

   =( 2 (5100)/(46.5. + 84.8))

   =8.8 m/s

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