Math homework help

Question

A cannon ball is fired from the top of a tower. The height, h, in metres, is modelled by the function h(t)=-2t²+20t+8 and t will always be greater than or equal to 0. I need to find the height of the tower, calculate the y value when x=5, find when the cannonball will hit the ground, and the y value of that time, calculate the maximum value, and determine the total time the cannonball was off of the ground.

Answer 1

h'(t) = -4t +20 = 0

t=5 seconds at max height

h(5) = -2(25) + 20(5) + 8 = 58 = max height

y=58 when t=5

it hits the ground when -2t^2 + 20t + 8= 0

t^2 -10t -4 = 0

t = 10/2 + or - (1/2)sqr(100+16)

= 5 + .5sqr116 = 5 + (1/2)10.77 = 5+5.38 = 10.38 seconds

at that time y=0