Tarzan, with a mass of 80.0 kg, wants to swing across a ravine on a vine, but th

Question

Tarzan, with a mass of 80.0 kg, wants to swing across a ravine on a vine, but the cliff on the far side of the ravine is 1.00 m higher than the cliff where Tarzan is now, and 1.90 m higher than Tarzan’s lowest point in his swing. Use g = 9.80 m/s2.
(a) If Tarzan wants to reach the cliff on the far side, how much kinetic energy (at least) must he have when he jumps off the cliff where he starts?
J
(b) How fast is Tarzan going at the bottom of his swing?
m/s
(c) If Tarzan swings along a circular arc of radius 9.00 m, what is the tension in the vine when Tarzan reaches the lowest point in his swing?
N

Explanation / Answer

a) His increase in potential energy must be m g h = 80 * 9.8 * 1 = 784 So he must have initially at least 784 J of KE b) He will obtain an additional KE of m g H = 80 * 9.8 * .9 = 706 His total KE at the bottom is 784 + 706 = 1490 1/2 m V^2 = 1490 and V = (2 * 1490 / 80)^1/2 = 6.1 m/s c) at the bottom T - m g = m V^2 / R solve for T

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