The height (in meters) of a shot cannonball follows a trajectory given by h(t) = -4.9t^2 + 14t - 0.4 at time (in seconds). For how many seconds is the height of the cannonball at least meters?
For how many seconds is the height of the cannonball at least meters?
Hello Guest!
How high should the cannonball at least fly? 6 meters. Thanks!
\(h(t) = -4.9t^2 + 14t - 0.4=6\)
\(h(t) = -4.9t^2 + 14t - 6.4=0\)
a b c
\(t = {-b \pm \sqrt{b^2-4ac} \over 2a}\)
\(t = {-14 \pm \sqrt{14^2-4\cdot (-4.9)\cdot (-6.4)} \over 2\cdot (-4.9)}\\ t=\dfrac{-14\pm 8.4}{-9.8}\\ \color{blue}t\in \{0.571,2.286\}\)
The cannonball is located at a height of 6 meters and above
from 0.57 seconds to 2.29 seconds after take-off, i.e. for 1.71 seconds.
!