Jacob kicks a soccer ball off the ground and into the air, with a velocity of 33 feet per second.

Question

Jacob kicks a soccer ball off the ground and into the air, with an initial velocity of 33 feet per second. Using the formula H(t) = -16^t + vt + s, what is the maximum height the soccer ball reaches? 

Answer 1

odds are you meant to write:

h(t) =-16t^2 +33t

take the derivative and set equal to zero

h'(t) = -32t + 33 = 0

t = 33/32 seconds at maximum height

h(33/32) = -16(33/32)^2 + 33(33/32) = -33^2/64 + 33^2/32 = 33^2/64 = 1089/64 = about about 17 feet in about 1 second = maximum height