A firework shell is fired from a mortar on the ground. Its hight is modeled by the function h=-16t^2+224t, where h is the height in feet and t is the time in seconds. If the shell does not explode, how long will it take for it to reach the ground?

1 Answer
Somebody N.
Jun 7, 2018

#color(blue)(14 " seconds")#

Explanation:

This is parabola of the form #nnn#. If we model this so the horizontal axis is the ground, then the period of time it takes to leave the ground and return again will be the roots of the given equation.

So we set #h=0#

#-16t^2+224t=0#

Factor:

#-16t(t-14)=0=>t=14 and t=0#

#t=0# is the starting point.

So the shell takes #14 " seconds"# to reach the ground.

This has been modelled on the shell being fired vertically at ground level level. In reality these problems have a angle of trajectory which changes the distance the shell will travel and the time it takes to reach the ground again.

PLOT:

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