A 50.4-kg circus performer is fired from a cannon that is elevated at an angle o

Question

A 50.4-kg circus performer is fired from a cannon that is elevated at an angle of 50.2 degree above the horizontal. The cannon uses strong elastic bands to propel the performer, much in the same way that a slingshot fires a stone. Setting up for this stunt involves stretching the bands by 2.68 m from their unstrained length. At the point where the performer flies free of the bands, his height above the floor is the same as that of the net into which he is shot. He takes 2.70 s to travel the horizontal distance of 29.8 m between this point and the net. Ignore friction and air resistance and determine the effective spring constant of the firing mechanism. Number Units the tolerance is +/-5%

Explanation / Answer

given, mass m = 50.4 kg
angle of cannon, theta = 50.2 degree above the horizontal
band strech, l = 2.68 m
time taken for horizontal displacement, t = 2.7 s
horizontal distance, d = 29.8 m
so horizontal velocity, vx = d/t = 11.037 m
so initial velocity, v = vx/cos(theta) = vx/cos(50.2) = 17.24 m/s
KE of the performer just before ejection from the cannon, KE 0.5mv^2 = 7491.981 J
this energy is provided by the band
so energy strored in band, 0.5kx^2 = 7491.981 [ k is effective spring constant of the band, x = l = 2.68 m]
so, k = 2086.2057 N/m

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