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# Pls help asap, i'm desperately needing you, i have no idea how to solve this....

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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  (in seconds). For how many seconds is the height of the cannonball at least  meters?

Nov 6, 2021

#1
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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.

!

Nov 6, 2021
edited by asinus  Nov 6, 2021
edited by asinus  Nov 6, 2021
#3
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6 meters

Guest Nov 6, 2021
#2
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6 meters, sir

Nov 6, 2021