If a football player passes a football from 4 feet off the ground with an initial velocity of 36 feet per second, how long will it take the football to hit the ground? Use the equation h = −16t2 + 6t + 4. Round your answer to the nearest hundredth.
A)0.72
B) 0.65
C)0.35
D)0.27

Option A: The football will take 0.72 seconds to hit the ground.

Explanation:

Given that the equation is

We need to determine how long will it take the football to hit the ground.

Let us substitute h = 0 in the above equation.

Thus, we have,

Now, we shall simplifying the equation using the quadratic formula.

The formula is given by

Substituting the values in the above formula, we get,

Simplifying, we get,

Taking out 2 as a common term, we get,

Dividing, we get,

Thus, the roots of the equation are

Simplifying the roots of the equation, we have,

and

Since, t cannot take a negative value, we have,

Therefore, the football will take 0.72 seconds to hit the ground.

Hence, Option A is the correct answer.

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