Question

A ball is thrown from a height of 25 meters with an initial downward velocity of 5/ms. The ball's height h (in meters) after t seconds is given by the following.

h=25-5t-5t^2
How long after the ball is thrown does it hit the ground?
Round your answer(s) to the nearest hundredth.

Answer 1

The ball hits the ground when h=0, 5(5-t-t²)=0.
t²+t-5=0. t²+t=5, t²+t+¼=5¼, (t+½)²=5¼.
t+½=±√(21/4)=±√21/2=±4.5826/2=±2.2913.
So t=-0.5 ±2.2913. We reject the negative solution because t starts from zero so negative values are out of range. Therefore t=1.79 seconds.