Equation given h(t)= -5t^2 +20t

Question

A football is kicked with a vertical speed speed of 20m/s, it’s height in h meters, after t seconds is given by the equation: h(t) = -5t^2 +20t. Determine how long the ball in the air and the maximum height the ball reached.

Answer 1

h=-5t^2+20t

h'= -10t+20=0

t= 20/10=2 sec to max height

double it to hit the ground = 4 seconds in the air

max h= h(2)= -5(2)^2 +20(2)= 20 meters high

or

-5t^2+20t

=-5(t^2 -4t+4) +20

= -5(t-2)^2 +20

vertex = (2,20)

t= 2 at max h = 20