Processing Math: Done
To print higher-resolution math symbols, click the
Hi-Res Fonts for Printing button on the jsMath control panel.

No jsMath TeX fonts found -- using image fonts instead.
These may be slow and might not print well.
Use the jsMath control panel to get additional information.
jsMath Control PanelHide this Message


jsMath

Lösung 1.1:3

Aus Online Mathematik Brückenkurs 2

Wechseln zu: Navigation, Suche

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

h(t)=1029.82t2=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)=ddt1029.82t2=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=196.414.0.

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