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 (see figure). Tarzan's mass is 79.7 kg, Jane's mass is 49.1 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 20.1 m. The length of the vine is 34.1 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

Final Energy Conservation

1/2*(mt+mj)*v2^2 = (mt+mj)*g*h

v2 = sqrt( 2*g*h )

v2 = sqrt(2*9.8*11.1)

v2 = 14.75 m/s

Conservation of Momentum

mt*v1 + mj*0 = (mt + mj)*v2

v1 = v2*(mt+mj)/mt

v1 = v2*(79.7 + 49.1)/79.7

v1 = 23.84 m/s

Initial Energy Conservation

mt*g*H + 1/2*mt*v0^2 = 1/2*mt*v1^2

Solve for v0:

v0 = sqrt( v1^2 - 2*g*H )

v0 = 13.2055 m/s

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