A 70.0kg circus performer is fired from a cannon that is elevated at an angle of

Question

A 70.0kg circus performer is fired from a cannon that is elevated at an angle of 40.0 degrees 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 3.00m from their unrestrained length. At that 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 2.14s to travel the horizontal distance of 26.8m between this point and the net. Ignore friction and air resistance and determine the effective spring constant of the firing mechanism.

Explanation / Answer

He travels at constant horizontal velocityof    26.8 / 2.14 =   12.523 m/s . His total initial velocity is    12.523 /cos40 =   16.348 m/s . His initial kinetic energy is   (1/2) mv2 = (1/2) * 70 * 16.3482 =    9354 Joules . The cannon also raises the person to a height of  3.00 sin40 = 1.9284 meters  before heis released. . So the cannon gives the person potential energyof    mgh = 70 * 9.80 * 1.9284 = 1323 Joules . Therefore the total energy stored in the bandswas    9354 + 1323 =   10677 Joules (the energy given to the person) . And the spring constant is found using    stored energy = (1/2) k x2    or .              10677 = (1/2) k 3.002 .    k =    2373 N/m

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