A trebuchet was a siege engine that used a falling counterweight to launch a pro

Question

A trebuchet was a siege engine that used a falling counterweight to launch a projectile. A schematic of a trebuchet Ls shown below (P Ls the projectile and C Ls the counterweight). For a given trebuchet, the counterweight Ls 2,000 kg and moves 5 m from its initial position while the projectile is being launched; the projectile is 100 kg and moves 15 m up while it is being launched. How fast is the the projectile launched? Assume the counterweight is 2 m from the pivot and the projectile is 10 m from the pivot and neglect the arm's mass.

Explanation / Answer

change in potential energy = KE

=> 2000*5*9.81 - 100*15*9.81 = 0.5*(2000*2*2 + 100*10*10)*w^2

=> w = sqrt(83385/9000) = 3.0438 rad/sec

=> V = wr = 3.0438*10 = 30.438 m/s Answer which is (A)

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