3. Tarzan, whose mass is Mr, swings on a vine to rescue Boy, whose mass is mg an

Question

3. Tarzan, whose mass is Mr, swings on a vine to rescue Boy, whose mass is mg and who is standing on the ground surrounded by snakes Tarzan (a) If the two must swing up to the branch of a tree a height h off the ground, from 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 mo, Mn boy snakes on the ground and h. (b) Tarzan has mass Mr= 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

a)

using conservation of energy

Potential energy of tarzan at height H = Potential energy of the two at height "h"

MT g H = (MT + mB) g h

H = (MT + mB) h/MT

b)

H = (MT + mB) h/MT = (80 + 40) (10)/(80) = 15 m

Vi = speed of tarzan just before grabbing the boy = sqrt(2 g H) = sqrt(2 x 9.8 x 15) = 17.15

V = final speed of the two after grabbing

using conservation of momentum

MT Vi = (MT + mB) V

V = MT Vi / (MT + mB) = 80 (17.15)/(80 + 40) = 11.4 m/s

force equation at the bottom is given as

T - (MT + mB)g= (MT + mB) V2 /L

T = (MT + mB)g + (MT + mB) V2 /L

T = (80 + 40) (9.8) + (80 + 40) (11.4)2/(30)

T = 1695.84 N

Since T < 2200 N

hence the vine does not break  

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