Question

A ball is thrown from the height of 35 meters with an initial downward velocity of 5m/s. The ball's height h (in meters) after t seconds is given below:
h=35-5t-5t^2
How long after the ball is thrown it hits the ground? Round to the nearest hundredth place.

Answer 1

You find this value by factoring.  Factoring finds the zeros of the function.  When the ball hits the ground, it has 0 height.  Therefore, when the function goes through the x axis, it has a y value of 0.  That means that when y = 0, the ball has hit the ground.  Use the quadratic formula to factor $h(t)=-5 t^{2}-5t+35$.  Notice I rearranged the terms.  When you factor that you get zeros of -3.19 and 2.19.  The two things in math that will never EVER be negative are time and distance/length.  Therefore, that tells us that the ball hits the ground 2.19 seconds after it was thrown.