An obnoxious brat assigns his 21.7-gram pet mouse Mickey the role of stunt mouse

Question

An obnoxious brat assigns his 21.7-gram pet mouse Mickey the role of stunt mouse by stuffing him into a spring gun and shooting him up into the air at some angle. The gun's spring has a force constant of 98.7 N/m and is initially compressed 14.1 cm. When Mickey reaches maximum height, he has a horizontal velocity with a speed of 2.37 m/s. How high above his initial location in the gun does Mickey soar? (In case you are worried, a miniature parachute opens at this point and Mickey lands safely. The brat is slightly less obnoxious than we thought.) Take g = 9.81 m/s2. Assume that the mass of the spring is small enough that the spring's change in potential energy during the spring's expansion is negligible.

Explanation / Answer

Seems like a conservation of energy problem.

1/2kx^2 = mgh +1/2mv^2

(1/2kx^2-1/2mv^2)/mg = h

((.5)(98.7)(.141)^2-1/2(.0217)(2.37)^2)/((.0217)*9.8) = h

h= 4.327 m

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