A 69.3-kg circus performer is firedfrom a cannon that is elevated at an angle of

Question

A 69.3-kg circus performer is firedfrom a cannon that is elevated at an angle of 40.4° above the horizontal. The cannon usesstrong elastic bands to propel the performer, much in the same waythat a slingshot fires a stone. Setting up for this stunt involvesstretching the bands by 3.03 mfrom their unstrained length. At the point where the performerflies free of the bands, his height above the floor is the same asthe height of the net into which he is shot. Hetakes 2.24 s to travel thehorizontal distance of 28.7 mbetween this point and the net. Ignore friction and air resistanceand determine the effective spring constant of the firingmechanism.
N/m

Explanation / Answer

Given :
If we use the principle of conservation of mechanical energy, theinitial elastic potential energy stored in the elasticbands
   must be equal to the sum of the kinetic energyand the gravitational potential energy of the performer at thepoint of
   ejection so that we get    (1 / 2) k x2 = (1 / 2) mvo2 + m g h    vo is the speed of the performerat the point of ejection    from the diagram we can also that    h = x sin    (1 / 2) k x2 = (1 / 2) mvo2 + m g x sin ........... (1)    if we take the horizontal motion of theperformer then we get    vox = vo cos........... (2)    vox = sx / t............ (3)    as from the given    sx = 28.7 m    so on combining the equations (2) and (3) weget    vo = sx / t(cos)    so we get    (1 / 2) k x2 = (1 / 2) m(sx2 / t2 cos2) +m g x sin    solving for k we get    k = m (sx / x tcos)2 + (2 m g sin / x)       = ......... N / m Solve it

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