A ball is thrown from a height of 40 meters with an initial downward velocity of 10 m/s. The balls height h (in meters) after t seconds is given by the following.

h = 40 - 10t - 5t^2

How long after the ball is thrown does it hit the ground?

Round to nearest hundredth

0=40-10t-5t^2

t^2+2t-8=0

(t+4) (t-2) = 0

t=-4 (not a solution) or t=2

Answer: after 2 seconds

First, set h (height) to 0, since that is the height we'll be solving for (at the ground). Factor the right side of the equation and set each individual binomial equal to zero. Solve for x in both equations and you should be left with a negative answer and a positive one. There is no negative time, so choose the answer that is positive.