A circus acrobat of mass M jumps straight up with initial speed V0 from a trampoline. While ascending, at a height h above the trampoline, he picks up a trained monkey of mass m that was hanging from a branch. What is the maximum height reached by the acrobat-monkey pair measured from the

Question

A circus acrobat of mass M jumps straight up with initial speed V0 from a trampoline. While ascending, at a height h above the trampoline, he picks up a trained monkey of mass m that was hanging from a branch. What is the maximum height reached by the acrobat-monkey pair measured from the branch?

Accepted Answer

(M / (M + m))² * (V0² / (2g) - h). The acrobat reaches height h with speed v1 = sqrt(V0² - 2gh). Grabbing the stationary monkey is a perfectly inelastic collision; by momentum conservation v2 = M*v1/(M+m). The pair then rises an additional height H = v2²/(2g) = M²*(V0²-2gh) / (2g*(M+m)²) = (M/(M+m))² * (V0²/(2g) - h).

A circus acrobat of mass M jumps straight up with initial speed V0 from a trampoline. While ascending, at a height h above the trampoline, he picks up a trained monkey of mass m that was hanging from a branch. What is the maximum height reached by the acrobat-monkey pair measured from the branch?

Solution

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