An obnoxious brat assigns his 20.7-gram pet mouse Mickey the role of stunt mouse

Question

An obnoxious brat assigns his 20.7-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 85.3 N/m and is initially compressed 14.1 cm. When Mickey reaches maximum height, he has a horizontal velocity with a speed of 2.21 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.

Explanation / Answer

using energy conservation,

kx2 /2 = mgh + mv2 /2

85.3 x 0.1412 /2 = (20.7/1000) x 9.8 x h + (20.7/1000) x 2.212 /2

0.848 = 0.20286h + 0.05055

h = 0.797/0.20286 = 3.93 m

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