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A ball with a mass of #360 g# is projected vertically by a spring loaded contraption. The spring in the contraption has a spring constant of #9 (kg)/s^2# and was compressed by #5/3 m# when the ball was released. How high will the ball go?

Answer 1

Charles Aeschliman

The height reached by the ball is #=3.54m#

The spring constant is #k=9kgs^-2#

The compression of the spring is #x=5/3m#

The potential energy stored in the spring is

#PE=1/2kx^2=1/2*9*(5/3)^2=12.5J#

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=0.360kg#

#PE_(ball)=12.5=0.360*9.8*h#

#h=12.5*1/(0.360*9.8)#

#=3.54m#

The height reached by the ball is #=3.54m#

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Answer 2

Axel Acevedo

The maximum height reached by the ball is approximately 0.77 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.