| Map dt Sapling Learning macmilan leaming Mickey, a daredevil mouse of mass m,

Question

| Map dt Sapling Learning macmilan leaming Mickey, a daredevil mouse of mass m, 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 k and is initially compressed a distance d from its relaxed position. If Mickey has a constant horizontal speed Vwhile he is flying through the air, how high above his initial location in the gun does Mickey soar? Find an expression for Mickey's maximum height hm in terms of m, V, d, k, and g.

Explanation / Answer

Given,

mass = m ; spring constant = k ; horizontal velocity = V ; distance = d ; and acceleration = g

from the conservation of energy

PE(spring) = PE(gravitational) + KE(of motion)

1/2 k d^2 = m g hm + 1/2 m V^2

m g hm = 1/2 k d^2 - 1/2 m V^2

solving for h we get

hm = (k d^2 - m V^2)/2mg

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