Tarzan, in one tree, sights Jane in another tree. He grabs the end of a vine wit

Question

Tarzan, in one tree, sights Jane in another tree. He grabs the end of a vine with length 18.5 m that makes an angle of 40 degree with the vertical, steps off his tree limb, and swings down and then up to jane's open arms. When he arrives, his vine makes an angle of 27 degrees with the vertical.

A.) Calculate Tarzan's potential and kinetic energies just before he steps off his limb. You can ignore air resistance and the mass of the vine.

B.) Calculate Tarzan's potential energy when he lands on jane's limb. Ignore air resistance and mass of the vine

C.) Determine whether Tarzan gives Jane a tender embrace or knocks her off her limb by calculating Tarzan's speed just before he reaches Jane. ignore air resistance and mass of vine.

Explanation / Answer

Let us assume, the end of vine, when hanging from tree, touches ground. Thus at 18.5 m down from the pivot point of the vine, the potential energy is zero (or can be taken as reference)

A) JUST BFORE he steps of, his kinetic energy = 0

potential energy = m*g*h = Mass of Tarzan * 9.8 * (18.5 - 18.5*(cos(40))

since mass of tarzan is not given, its potential energy cannot be calculated!

B) potential energy when landing on Jane's limbs = m*g*h = Mass of Tarzan * 9.8 * (18.5 - 18.5*(cos(27))

C) let the speed be v

1/2*m*v^2 = K.E gained = P.E lost = m*g*(18.5(cos(27) - cos(40)))

v = sqrt(2*9.8*(18.5(cos(27) - cos(40)))) = 6.73 m/s = 24.23 km/hr. Thus implies, Tarzan will knock off her limb

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