A football is kicked from ground level with an initial vertical velocity of 32ft/sec. after how many seconds will the football hit the ground

Question

How long will it take for the football to hit the ground 

Answer 1

The height of the football as a function of time obeys the equation:

 

h(t) = (1/2)at² + v₀t + h₀

 

where 

 

t = time since kick, in seconds

a = -g = -32 ft/s²

v₀ = 32 ft/s

h₀ = 0 if kicked from the ground

 

Then

 

h(t) = -16t² + 32t

 

The ball hits the ground when h(t) = 0:

 

0 = -16t² + 32t

 

Just solve for t.  You will get two solutions.  One will be t = 0, the other will be a t > 0.  The t = 0 solution is the moment the ball is kicked from the ground.  The t > 0 solution is the moment the ball hits the ground on the way down.  Find the t > 0  solution to the equation above and that will be the answer you seek.