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A ball with a mass of #144 g# is projected vertically by a spring loaded contraption. The spring in the contraption has a spring constant of #36 (kg)/s^2# and was compressed by #6/4 m# when the ball was released. How high will the ball go?

Answer 1

Nathan Ashcroft

The height is #=57.4m#

The spring constant is #k=36kgs^-2#

The compression is #x=6/4=3/2m#

The potential energy is

#PE=1/2*36*(3/2)^2=81J#

This potential energy will be converted to kinetic energy when the spring is released and to potential energy of the ball

#KE_(ball)=1/2m u^2#

Let the height of the ball be #=h #

The acceleration due to gravity is #g=9.8ms^-2#

Then ,

The potential energy of the ball is #PE_(ball)=mgh#

Mass of the ball is #m=0.144kg#

#PE_(ball)=81=0.144*9.8*h#

#h=81*1/(0.144*9.8)#

#=57.4m#

The height is #=57.4m#

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Answer 2

Adam Arnold

The ball will reach a height of 0.27 meters.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.