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

Answer:

A. 0.72

Step-by-step 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

Answer:

A. 0.72

Step-by-step 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:

$ax^{2} + bx + c, a\neq0$.

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:

$x_{1} = \frac{-b + \sqrt{\bigtriangleup}}{2*a}$

$x_{2} = \frac{-b - \sqrt{\bigtriangleup}}{2*a}$

$\bigtriangleup = b^{2} - 4ac$

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).

$t = \frac{-6 - \sqrt{292}}{-32} = 0.72$

The correct answer is:

A. 0.72