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 4 meters?
+128474 -4.9t^2 + 14t - .04 = 4
-4.9t^2 + 14t -.04 - 4 = 0
-4.9t^2 + 14t - 4.4 = 0 multiply through by -10
49t^2 - 140t + 44 = 0
Solving this with the quadratic formula we get
t ≈ .36 sec
and
t ≈ 2.5 sec
It is above 4 m for about 2.5 - .36 = 2.14 seconds = 214/100 = 107/50 sec
