A cannonball fired out to sea from a shore battery follows a

A cannonball fired out to sea from a shore battery follows a parabolic trajectory given by the graph of the equation h(x) = 9x 0.01x2 where h(x) is the height of the cannonball above the water when it has traveled a horizontal distance of x feet. (a) What is the maximum height that the cannonball reaches? ft (b) How far does the cannonball travel horizontally before splashing into the water? ft

Solution

h(x) = 9x 0.01x^2 where h(x) is the height of the cannonball above the water when it has traveled a horizontal distance of x feet

a) Maximum height for parabolic function occurs at vertex.

x = -b/2a = -(9)/(2*(-0.01))

= 9/0.02 = 450 feet

b) How far does the cannonball travel horizontally before splashing into the water?

h(x) =0

9x 0.01x^2 =0

9x = 0.01x^2

x^2 = 9/0.01

x = 3/0.1 = 30 feet horizontally