Identify the function that models (ignoring air resistance) a ball being thrown in the air with an initial velocity of 32 ft/s, from a height of 20 feet.

h(t) = 20 + 32t - 16t²

Explanation:

The function that models the motion of an object thrown in the air (vertically) is:

h(t) = H + Vo × t - (1/2) g×t²

Where:

H is the initial height = 20 feet
Vo is the inital velocity = 32 ft/s (positive if it is upward)
g is gravity acceleration ≈ 32 ft/s²
t is the time

Substitute values:

h(t) = 20 + 32t - 32t² / 2

h(t) = 20 + 32t - 16t²

That is the answer.

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