A ball with a mass of #80 g# is projected vertically by a spring loaded contraption. The spring in the contraption has a spring constant of #16 (kg)/s^2# and was compressed by #1/5 m# when the ball was released. How high will the ball go?

Answer 1

I tried this but check my maths.

We can consider:

So basically we can write:
#1/2kx^2=1/2mv^2#
#v=sqrt((kx^2)/m)=sqrt(8)=2.8m/s#

We now use the kinematic relationship:
#v_f^2=v_i^2+2ah#
With #a=# acceleration of gravity downwards and #v_f=0# for the final velocity;
#0=8-(2*9.8*h)#
#h=8/(2*9.8)=0.4m#
If we consider also the initial compression, the total vertical distance should be:
#h+h_1=0.4+0.2=0.6m#

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Answer 2

Olivia Askew

The maximum height the ball will reach is approximately 0.39 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.