The maximum height is determined by using the given equation as written below.
h(t) = -16t² + 45t + 40
We derive the equation in terms of t and equate the differential to zero.
dh(t) = -32t + 45
0 = -35t + 45
Transpose the constant to the other side of the equation.
35t = 45
Divide the equation by 35, giving us the value of t which is equal to 9/7.
This means that the maximum height is attained after 9/7 seconds.
Substitute the computed time to the equation for height.
h(9/7) = -16(9/7)² + 45(97) + 40
The value of h is equal to 71.41 ft.
ANSWER: 71.41 ft