In an effort to win Lister dodgeball once and for all, you design a clever, spri

Question

In an effort to win Lister dodgeball once and for all, you design a clever, spring-loaded, buried cannon that fires a dodgeball. The cannon is frictionless and buried in the ground at an angle 0-30.6 with respect to the horizontal. Inside the cannon is a spring with spring constant 383.8 N/m and an equilibrium length equal to the length of the cannon. A dodgeball (mass m-0.325 kg) is pushed into the cannon a distance a = 1.333 m and released. Once launched from the end of the tube (at ground level) what is the range of dodgeball? Assume that the tube is frictionless and the assumptions of projectile motion apply during the dodgeball's flight. Express your answer in metres

Explanation / Answer

By conservation of energy

(1/2)kd2=mgdsin30.6+(1/2)mV2

(1/2)*383.8*1.3332=0.325*9.81*1.333*sin30.6+(1/2)*0.325*V2

V=45.66 m/s

range of projectile is given by

R=V2sin(2o)/g =45.662sin(2*30.6)/9.81

R=186.25 m

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