Verified answer

As the ball moves upward, the vertical velocity decreases due the downward attraction force between the ball and the earth. When the ball reaches the maximum height, the vertical velocity is 0 ft/s.

H = 6t^2 + 40t + 5

In physics, the following equation is used to determine the final position of an object.

d = Initial position + initial velocity * time + ½ * acceleration * time^2

For this problem, the coefficient of t^2 is 6. So ½ * a = 6

Acceleration = 12 ft/s^2, Initial velocity = 40 ft/s, Initial height = 5 ft

For change of velocity, use the equation below.

Final velocity = Initial velocity + acceleration * time

Since the direction of the acceleration is always toward the surface of the earth, the velocity must decrease at the rate of 12 ft/s^2. This means the acceleration must be -12ft/s^2. So the coefficient of t^2 must be -6.

H = -6t^2 + 40t + 5

Final velocity = 40 + -12 * time

When the ball reaches the maximum height, the vertical velocity is 0 ft/s.

0 = 40 – 12 * t

40 = 12 * t, Time = 40/12 = 3⅓ seconds

Maximum height = (-6 * 3⅓^2)+ (40 * 3⅓) + 5

Maximum height = -66⅔ + 133⅓ + 5

Maximum height = 71⅔ ft

This looks more like Algebra 2 than physics.