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Tarzan, in one tree, sights jane in another tree. he grabs the end of a vine with length 20 m that makes an angle of 45â 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 30â with the vertical. determine whether he gives her a tender embrace or knocks her off her limb by calculating tarzan’s speed just before he reaches jane. you can ignore air resistance and the mass of the vine.

Verified Answer :

syed514

Vertical height (initial) = L - LcosA = L(1-cos45) = 20 x 0.29 = 5.8m 
Vertical height (final) = L(1-cos30) = 20 x 0.13 = 2.6m 
Loss in vertical height = 5.8 - 2.6 = 3.2m 
=>Loss in PE = Gain in KE, Let the final velocity of the Tarzan is v m/s 
=>m x g x h = 1/2 x m x v^2 
=>v = sqrt[2gh] = sqrt[2 x 9.8 x 3.2] = 7.91 m/s 
This a quite good speed to knock off Jane from the tree.

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