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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?

Jun 14, 2021

#1
+33757
+2

Use 8.7 as h

8.7 = -4.9t^2 + 14t - 0.4        re-arrange to:

-4.9t^2 + 14t - 9.1                 Now use Quadratic Formula to find the solution values of 't'    subtract the smaller from the larger for your answer

a = -4.9       b = 14        c = -9.1

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

Jun 14, 2021

#1
+33757
+2

Use 8.7 as h

8.7 = -4.9t^2 + 14t - 0.4        re-arrange to:

-4.9t^2 + 14t - 9.1                 Now use Quadratic Formula to find the solution values of 't'    subtract the smaller from the larger for your answer

a = -4.9       b = 14        c = -9.1

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

ElectricPavlov Jun 14, 2021