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The height h, in feet, of a ball that is released 4 ft above the ground with an initial upward velocity of 80 ft/s is a function of the time t, in seconds, the ball is in the air and is given by the following.

h(t) = −16t^2 + 80t + 4, 0 ≤ t ≤ 5.04

(a) Find the height of the ball (in feet) above the ground 2 s after its released.

(b) Find the height of the ball (in feet) above the ground 4 s after its released.

The given equation is where h is the height, in feet, of a ball and t is the time, in seconds.

Part a: The height of the ball when t = 2 seconds:

The height of the ball above the ground 2 seconds after it is released can be determined by substituting t= 2 in the equation , we get;

Simplifying the terms, we get;

Thus, the height of the ball after 2 seconds is 100 feet.

Part b: The height of the ball when t = 4 seconds:

The height of the ball above the ground 4 seconds after it is released can be determined by substituting t = 4 in the equation , we get;

Simplifying the terms, we get;

Thus, the height of the ball after 4 seconds is 68 feet.

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