Swing Set Height
Tarzan and Jane Physics Question- how to set it up!?
Tarzan and Jane, whose total mass is 137 kg, start their swing on a 4.6 m. long vine when the vine is at an angle 32.6 degrees with the horizontal. At the bottom of the arc, Jane, whose mass is 47 kg, releases the vine. Acceleration of gravity is 9.81 m/s^2. What is the maximum height at which Tarzan can land on a branch after her swing continues? (Hint: Treat Tarzan’s and Jane’s energies as separate quantities.) Answer in units of m.
Thank you very much for your help in advance!
At the beginning, Tarzan and Jane have a potential energy of
{(M(T) + M(J) }(g) (4.6) ( 1 – sin 57.4 deg) which is M(both)gh.
At the bottom, they are traveling at a velocity V where all the P.E. has been converted to Kinetic Energy:
V^2 = { 2(137)(4.6)(1-sin57.4)/137 }; (from (1/2)MV^2 = KE )
Tarzan’s KE is (1/2)(90)V(T)^2 = 4.6(1-sin57.4) and equals his P.E. at the highest point he will reach, H where V(T) = Tarzan’s velocity after Jane lets go the vine.
Momentum must be conserved so we get
M(T)V(T) + M(J)V(J) = M V = {M(T) + M(J)}V where V is obtained from the P.E. above. We can get V(J) in terms of V(T)
and use (1/2)M(T){ V(T)}^2 = (1/2)(M)V^2 – (1/2)M(J) {V(J)}^2
to get V(T) to use in M(T)gH = (1/2){M(T)} [V(T)]^2
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