QuestionJune 10, 2025

A cell phone falls off a balcony. It's height (in feet)is given by the formula f(t)=-16t^2+13.4t+150 , where t is measured in seconds. How long will it take the cell phone to hit the ground? Round your answers to three decimal places.

A cell phone falls off a balcony. It's height (in feet)is given by the formula f(t)=-16t^2+13.4t+150 , where t is measured in seconds. How long will it take the cell phone to hit the ground? Round your answers to three decimal places.
A cell phone falls off a balcony. It's height (in feet)is given by the formula f(t)=-16t^2+13.4t+150 , where t is measured in seconds. How long will it take the cell phone to hit the ground? Round your answers to three decimal places.

Solution
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Answer

3.515 seconds Explanation 1. Set the height equation to zero To find when the cell phone hits the ground, set f(t) = 0: -16t^2 + 13.4t + 150 = 0. 2. Use the quadratic formula **Quadratic Formula**: t = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}, where a = -16, b = 13.4, and c = 150. 3. Calculate the discriminant Discriminant \Delta = b^2 - 4ac = (13.4)^2 - 4(-16)(150). \Delta = 179.56 + 9600 = 9779.56. 4. Solve for t using the quadratic formula t = \frac{-13.4 \pm \sqrt{9779.56}}{-32}. Calculate \sqrt{9779.56} \approx 98.89. t_1 = \frac{-13.4 + 98.89}{-32} and t_2 = \frac{-13.4 - 98.89}{-32}. t_1 \approx -2.673 (not valid as time cannot be negative). t_2 \approx 3.515.

Explanation

1. Set the height equation to zero<br /> To find when the cell phone hits the ground, set $f(t) = 0$: $-16t^2 + 13.4t + 150 = 0$.<br />2. Use the quadratic formula<br /> **Quadratic Formula**: $t = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$, where $a = -16$, $b = 13.4$, and $c = 150$.<br />3. Calculate the discriminant<br /> Discriminant $\Delta = b^2 - 4ac = (13.4)^2 - 4(-16)(150)$.<br /> $\Delta = 179.56 + 9600 = 9779.56$.<br />4. Solve for t using the quadratic formula<br /> $t = \frac{-13.4 \pm \sqrt{9779.56}}{-32}$.<br /> Calculate $\sqrt{9779.56} \approx 98.89$.<br /> $t_1 = \frac{-13.4 + 98.89}{-32}$ and $t_2 = \frac{-13.4 - 98.89}{-32}$.<br /> $t_1 \approx -2.673$ (not valid as time cannot be negative).<br /> $t_2 \approx 3.515$.
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