Tarzan swings on a vine from a cliff to rescue Jane, who is standing on the grou

Question

Tarzan swings on a vine from a cliff to rescue Jane, who is standing on the ground surrounded by snakes. His plan is to push off the cliff, grab Jane at the lowest point of his swing, and carry them both to the safety of a nearby tree. Tarzan's mass is 76.7 kg, Jane's mass is 43.9 kg, the height of the lowest limb of the target tree is 11.1 m, and Tarzan is initially standing on a cliff of height 20.3 m. The length of the vine is 35.1 m. With what speed should Tarzan push off the cliff if he and Jane are to make it to the tree limb successfully?

Explanation / Answer

to reach the tree safely

kinetic energy at ground = potential energy at tree

0.5 x ( 76.7 + 43.9) x v^2 = ( 76.7 + 43.9) x 9.8 x 11.1

velocity at bottom after tarzon grab zane v = 14.75 m/s

conserving momentum at lowest point

76.7 x v1 = 120.6 x 14.75

velocity of tarzon before grabing zane v1 = 23.19 m/s

now again conserving energy for tarzon from cliff to ground

potential energy at cliff + kinetic energy at cliff = kinetic energy at bottom

76.7 x 9.8 x 20.3 + 0.5 x 76.7 x (v2)^2 = 0.5 x 76.7 x (23.19)^2

speed of tarzon with which he must push cliff v2 = 11.82 m/s

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