Aball is thrown from a height of 43 meters with an initial downward velocity of 4 m/s. the ball's height h (in meters) after t seconds is given by the following. h=43-4t-5t^2 how long after the ball is thrown does it hit the ground?

When the ball will hit the ground, the height will be zero. So we need to replace  with 0 in our equation, and solve for :


To solve this equation we are going to use the quadratic formula: .
From our height equation, we can infer that , , and . So lets replace those values in our quadratic formula to find 

or 
or 
Since time cannot be negative,  is the solution of our equation.

We can conclude that the ball will hit the ground after 2.71 seconds.