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 janeâ€™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 tarzanâ€™s speed just before he reaches jane. you can ignore air resistance and the mass of the vine.

Question

Physics

Genevieve Alvarado

Today, 11:21

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 janeâ€™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 tarzanâ€™s speed just before he reaches jane. you can ignore air resistance and the mass of the vine.

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Eileen · Answer 1

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.