Mickey, a daredevil mouse of mass 0.0181 kg, is attempting to become the world\'

Question

Mickey, a daredevil mouse of mass 0.0181 kg, is attempting to become the world's first "mouse cannonball." He is loaded into a spring-powered gun pointing up at some angle, and is shot into the air. The gun's spring has force constant of 58.3 N/m and is initially compressed a distance of 0.125 m from its relaxed position. If Mickey has a constant horizontal speed of 2.19 m/s while he is flying through the air, how high above his initial location in the gun does Mickey soar? Take g = 9.81 m/s^2. 2.063 m

Explanation / Answer

Given

conservation of energy, elastic potential energy = k.e + p.e_g

   0.5*kx^2 = 0.5*mv^2 +mgh

   h = 0.5(kx^2 - mv^2) /mg

   h = (0.5*58.3*0.125^2 - 0.0181*2.19^2)/(0.0181*9.8) m

   h = 2.0783591160 m
   h = 2.1 m

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