1. When a cannonball is fired, the equation of its pathway can be modeled by h = - 1612 + 128t.

a) Find the maximum height of the cannonball.

The maximum height of the ball is 256m

Step-by-step explanation:

Given the equation of a pathway modelled as pathway can be modeled by h = - 16t² + 128t

At maximum height, the velocity of the ball is zero.

velocity = dh/dt

velocity = - 32t + 128

Since v = 0 at maximum height

0 = - 32t+128

32t = 128

t = 128/32

t = 4seconds

The maximum height can be gotten by substituting t = 4 into the modelled equation.

h = - 16t² + 128t

h = - 16 (4) ²+128 (4)

h = - 16 (16) + 512

h = - 256+512

h = 256m