Lösung 1.1:3

Aus Online Mathematik Brückenkurs 2

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

ht=10−2982t2=0 

This second-degree equation has the solutions

t=982210 

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,

vt=ht=ddx10−2982t2=−982t 

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

v982210=−982982210=−9822982210=982210=−1964−140 

The minus sign shows that the speed is directed downwards, and the ball's speed is therefore 140 m/s.