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The height (in meters) of a shot cannonball follows a trajectory given by h(t) = -4.9t^2 + 14t - 0.4 at time t (in seconds). As an improper fraction, for how long is the cannonball above a height of 8.7 meters?

Jan 3, 2022

#1
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h = 8.7 m

8.7 = -4.9t^2 + 14 t -.4

0 = -4.9 t^2 + 14 t - 9.1         Now use Quadratic Formula to solve for t's    the time above 8.7 m is the time between the t's

a = -4.9     b = 14     c = - 9.1

$$t = {-14 \pm \sqrt{(14)^2-4(-4.9)(-9.1)} \over 2(-4.9)}$$

Jan 3, 2022