An obnoxious brat assigns his 18.3-gram pet mouse Mickey the role of stunt mouse

Question

An obnoxious brat assigns his 18.3-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 88.9 N/m and is initially compressed 14.9 cm. When Mickey reaches maximum height, he has a horizontal velocity with a speed of 2.45 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

The Spring energy equals the Kinetic energy of the mouse when leaving the spring.

Spring energy = .5kx2    KE = .5mv2

So .5kx2 = .5mv2

v = (kx2/m)   = [(61.7)(.123)2/(.0205)]    =   6.75 m/s

In the x direction, the velcocity remains constant, and vx is found by

vx = vcos

cos = vx/v

= cos-1 (2.15)/(6.75) = 71.43o

In the y direction, the vy = vsin   vy = 6.75(sin 71.43) = 6.40 m/s

In the y direction, at the top of the path, the velocity will be zero, so...

vf2 = vo2 +2ad

d = (6.40)2/(2)(9.81)

d = 2.09 m

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