Physics

In a stunt, three people jump off a platform and fall 9.9 m onto a large air bag. A fourth person at the other end of the air bag, the "flier," is launched 19 m vertically into the air. Assume all four people have a mass of 67 kg.

a. What fraction of the mechanical energy of the three jumpers is transferred to the mechanical energy of the flier?
(Express your answer to two significant figures.)

b. What is the total momentum of the three jumpers just before they land on the air bag? Let upward be the positive direction.
(Express your answer to two significant figures and include appropriate units.)

c. What is the momentum of the flier just after launch? Let upward be the positive direction.
(Express your answer to two significant figures and include appropriate units.)

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  1. a. Initial gravitational potential energy = 3*67 kg*9.8 m/s^2*9.9 m = 19501 J
    Final GPE = 1*67 kg*9.8 m/s^2*19 m = 12475 J
    fraction of the mechanical energy = 12475 J / 19501 J = 64/100 = 0.64

    b. 3 jumper,s initial gravitational potential energy = final kinetic energy
    19501 J = 1/2 * 3*67 kg*v^2
    v^2 = 2*19501 J / (3*67 kg) = 194 J/kg
    v = -13.93 m/s

    Initial momentum = 3*67 kg*(-13.93 m/s) = -2800 kg.m/s

    c. flier,s final GPE = initial KE
    12475 J = 1/2 *67 kg*v^2
    v^2 = 2*12475 J / 67 kg = 373.4 J/kg
    v = 19.30 m/s
    Initial momentum = 67 kg*19.30 m/s = 1293 kg.m/s ~= 1300 kg.m/s

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    posted by Wasif

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