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# A ball is thrown from an initial height of 3 meters

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A ball is thrown from an initial height of 3 meters with an initial upward velocity of 20m/s. The ball's height (in meters) after seconds is given by the following h=3+20t-5t^2. Find all values of for which the ball's height is 13 meters.

Feb 15, 2021

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h=3+20t-5t^2.       looking for h = 13

13=3+20t-5t^2      re-arrange a bit

-5t2 +20t -10 = 0         divide by -5

t2 -4t +2 = 0    use Quadratic Formula

a = 1      b = -4        c = 2

$$t= {-4 \pm \sqrt{(-4)^2-4(1)(2)} \over 2(1)}$$

Feb 15, 2021