Question

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.

Answer 1

Rounding to the nearest hundredth, it is 0.72

Answer 2

0.723 seconds

Explanation:

Let h = 0

0 = -16t² + 6t + 4

Let’s solve by completing the square.

Subtract 4 from both sides.

-4 = -16t² + 6t

Since the coefficient of -16t² is -16, divide both sides by -16.

1/4 = t² - 3/8t

The coefficient of (-3)/8t is (-3)/8. Let b=(-3)/8.

Then we need to add (b/2)² = 9/256 to both sides to complete the square.

Add 9/256 to both sides.

73/256 = t² - 3/8t + 9/256

Factor right side.

73/255 = (t-3/16)²

Take the square root on both sides.

±√(73/255) = t-3/16

Add 3/16 to both sides.

3/16 ± √(73/255) = t

The answer has to be positive, not negative.

0.72254626884 = t

0.723 ≈ t