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Aus Online Mathematik Brückenkurs 2

The ball hits the ground when its height is zero, i.e. when

h(t)=10−29.82t2=0.

This quadratic equation has the solutions

t=9.82210

where the positive root is the time when the ball hits the ground.

We obtain the ball's speed as a function of time as the time derivative of the height,

v(t)=h(t)=ddt10−29.82t2=−9.82t.

If we substitute the time when the ball hits the ground, we obtain the ball's speed at that instant,

v9.82210=−9.829.82210=−9.8229.82210=9.82210=−196.4−14.0.

The minus sign indicates that the speed is directed downwards, and the ball's speed is therefore 14.0 m/s.