Question

question 1 (multiple choice worth 2 points) (02.08 mc) if a football player passes a football from 4 feet off the ground with an initial velocity of 6 feet per second, how long will it take the football to hit the ground? use the equation ( h = - 16 t ^ { 2 } + 6 t + 4 ). round your answer to the nearest hundredth. 0.72 0.65 0.35 0.27

Explanation:

Step1: Set up the equation

When the football hits the ground, \(h = 0\). So we have the quadratic equation \(0=-16t^{2}+6t + 4\). In the general form \(ax^{2}+bx + c = 0\), here \(a=-16\), \(b = 6\), \(c = 4\).

Step2: Apply the quadratic formula

The quadratic formula is \(t=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}\).
Substitute \(a=-16\), \(b = 6\), \(c = 4\) into the formula:

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We have two solutions for \(t\):
\(t_{1}=\frac{-6 + 2\sqrt{73}}{-32}\) and \(t_{2}=\frac{-6-2\sqrt{73}}{-32}\)
Calculate \(t_{1}=\frac{-6 + 2\sqrt{73}}{-32}\approx\frac{-6+17.15}{-32}\approx - 0.35\) (rejected since time cannot be negative)
Calculate \(t_{2}=\frac{-6 - 2\sqrt{73}}{-32}=\frac{6 + 2\sqrt{73}}{32}\approx\frac{6+17.15}{32}\approx0.72\)

Answer:

0.72