A 70-kg circus performer is fired from a cannon that is elevated at an angle of

Question

A 70-kg circus performer is fired from a cannon that is elevated at an angle of 38° 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 3.7 m from their unstrained length. He takes 4.7 s to travel between the launch point (where he is free from the bands) and the net into which he is shot. Assume the launch and landing points are at the same height and do not neglect the change in height during stretching. What is the launch speed? (Ignore friction and air resistance.) m/s What is the effective spring constant of the firing mechanism? N/m

Explanation / Answer

given

theta = 38 degrees

time of flight, T = 4.7 s

m = 70 kg

x = 3.7 m

a) let vo is the launch speed.

we know, T = 2*vo*sin(theta)/g

==> vo = T*g/(2*sin(theta))

= 4.7*9.8/(2*sin(38))

= 37.4 m/s

b) let k is the effective spring constant.

now apply conservation of energy

(1/2)*k*x^2 = (1/2)*m*v^2

k = m*v^2/x^2

= 70*37.4^2/3.7^2

= 7152 N/m

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