swings on a vine Tarzan, whose mass is M to rescue Boy, whose mass is mg and who

Question

swings on a vine Tarzan, whose mass is M to rescue Boy, whose mass is mg and who is standing on the ground surrounded by snakes. 3, Tarzan (a) If the two must swing up to the branch of a tree a height h off the ground, frorm what minimum height H above the ground must Tarzan start his swing? Assume that Tarzan starts from rest and that he grabs Boy at the lowest point of his swing. Answer in terms of mp Mp and h. boy snakes on the ground (b) Tarzan has mass M,-80 kg, Boy has mass m,-40 kg, the tree branch has height h = 10 m, and the vine has length L- 30 m. The height of the cliff, H, is given by your answer to part (a). If the vine has a breaking strength of 2200 N, does it break after Tarzan has grabbed Boy? Consider the instant immediately after he has grabbed Boy, when the vine is vertical.

Explanation / Answer

Speed of tarzan at the lowest point,

v = sqrt(2 g H )

now applying momentum conservation,

M sqrt(2 g H) + 0 = (M + m) vf

vf = (M / (M + m)) sqrt(2 g H)

Applying energy conservation again,

vf^2 / 2 = g h

((M / (M + m)) )^2 g H = g h

H = ( ( M + m) / M)^2 h ..........Ans

(b) H = (120 / 80)^2 x 10 = 22.5 m

vf = sqrt(2 x 9.81 x10) = 14 m/s

and a = v^2 / r = 6.54 m/s^2

T - (M + m) g = ( M + m ) a

T = (80 + 40 (9.81 + 6.54 ) = 1962 N

No, it will not break,

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