Question

You hit a golf ball into the air from a height of inches above the ground, with an initial velocity of 85 ft/s. The function is h= -16t^2+85t+1/12, models the height, in feet, of the ball at time ¨t¨, in seconds. Will the ball ever reach a height of 125 ft?

Answer 1

The ball will not get up to 125 ft

Explanation:

The initial velocity of the golf ball = 85 ft/s

The function for the height, h, in feet, of the golf ball is h = -16·t² + 85·t + 1/12

Where;

t = The time in seconds of flight of the golf ball

We have at maximum height, dh/dt = 0, which gives;

dh/dt = d(-16·t² + 85·t + 1/12)/dt = 0

-32·t + 85 = 0

t = 85/32

Given that d²h/dt² = d(-32·t + 85)/dt = -32 which is negative, the obtained point, t = 85/32, above is a maximum point

Substituting the value of t at the maximum into the function for the height h, to obtain the value for the maximum height, we have;

h
`_((max))` = h(85/32) = -16 × (85/32)² + 85× (85/32) + 1/12 ≈ 112.974

The maximum height reached = h
`_((max))` = 112.974 ft.

The maximum height reached ≈ 112.974 ft

Therefore, the ball will not get up to 125 ft.