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Lösung 1.1:3

(Unterschied zwischen Versionen)

Version vom 10:00, 11. Mär. 2009

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

9.822

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)=ddt

10−29.82t2

=−9.82t.

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

9.822

=−9.82

9.822

10=−

9.822

10=

9.82

10=−

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.