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The equation y = -4.9t^2 - 3.5t + 12.4 relates the height y (in meters) to the elapsed time t (in seconds) for a ball thrown downward at 3.5 meters per second from a height of 12.4 meters from the ground. In how many seconds will the ball hit the ground? Express your answer as a decimal rounded to the nearest hundredth.

Jul 6, 2021

#1
+234
+2

Just a quadratic, so we have,

$$-4.9t^2 - 3.5t + 12.4 = 0$$

$$x = {-b \pm \sqrt{b^2-4ac} \over 2a}$$

$$x = {3.5 \pm \sqrt{255.29} \over -9.8}$$

Simplify via calculator we get roots, $$x = -1.99, 1.28$$. We want the positive root so the answer is 1.28

Jul 6, 2021

#1
+234
+2

Just a quadratic, so we have,

$$-4.9t^2 - 3.5t + 12.4 = 0$$

$$x = {-b \pm \sqrt{b^2-4ac} \over 2a}$$
$$x = {3.5 \pm \sqrt{255.29} \over -9.8}$$
Simplify via calculator we get roots, $$x = -1.99, 1.28$$. We want the positive root so the answer is 1.28