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.

Choose one:
A. 0.72
B. 0.65
C. 0.35
D. 0.27

Answer 1

A. 0.72

Explanation:

When the ball hits the ground, h = 0.

0 = -16t² + 6t + 4

0 = 8t² − 3t − 2

Solve with quadratic formula:

t = [ 3 ± √(9 − 4(8)(-2)) ] / 16

t = (3 ± √73) / 16

t = 0.72

Answer 2

A. 0.72

Explanation:

The football is going to hit the ground when
`h = 0`.

So we have to solve the following second order polynomial.

`-16t^(2) + 6t + 4 = 0`

We do this by the bhaskara formula.

Explanation of the bhaskara formula:

Given a second order polynomial expressed by the following equation:

`ax^(2) + bx + c, a\\eq0`.

This polynomial has roots
`x_(1), x_(2)` such that
`ax^(2) + bx + c = (x - x_(1))*(x - x_(2))`, given by the following formulas:

`x_(1) = (-b + √(\bigtriangleup))/(2*a)`

`x_(2) = (-b - √(\bigtriangleup))/(2*a)`

`\bigtriangleup = b^(2) - 4ac`

For the polynomial
`-16t^(2) + 6t + 4 = 0`, we have that:

`a = -16, b = 6, c = 4`.

So

`\bigtriangleup = 6^(2) - 4(-16)(4) = 292`

The solution is the positive root(there is no negative time).

`t = (-6 - √(292))/(-32) = 0.72`

The correct answer is:

A. 0.72