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?

Guest Nov 6, 2021

#1**+1 **

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.

!

asinus Nov 6, 2021