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The equation y = -16t^2 - 80t + 54 describes the height (in feet) of a ball thrown downward at 80 feet per second from a height of 54 feet from the ground, where t represents time, measured in seconds. In how many seconds will the ball hit the ground? Express your answer as a decimal rounded to the nearest hundredth.

Jul 11, 2021

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When the ball hits the ground, height = y   will be ZERO

0 = - 16t^2 - 80t + 54         Use quadratic equation    a = -16      b = -80    and   c = 54   to solve for t

throe out the negative 't' value

$$t = {80 \pm \sqrt{(-80)^2-4(-16)(54)} \over 2(-16)}$$

You need to know how to calculate using the Quadratic Formula......if you already do, then here is a quick and easy Quadratic Formula calculator that I often use :