A 74.9-kg circus performer is fired from a cannon that is elevated at an angle o

Question

A 74.9-kg circus performer is fired from a cannon that is elevated at an angle of 36.8° 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 3.15 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 the height of the net into which he is shot. He takes 2.24 s to travel the horizontal distance of 24.7 m between this point and the net. Ignore friction and air resistance and determine the effective spring constant of the firing mechanism.

Explanation / Answer

the horizontal speed is Vx = X /t = 24.7 / 2.24 = 11.027m/s initial velocity with which the performer was fired is V = Vx / cos 36.8 = 11.027 / cos 36.8 = 13.77m/s According to conservation of energy (1/2) kx^2 = (1/2) mV^2 K = mV^2 / x^2 = (74.9)(13.77)^2 / (3.15)^2 = 1431.5 N/m

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