SOLUTION: The height in feet of a fireworks shell can be modeled h(t) = -16t2+224t , where t is the time in seconds after it is fired.Find the maximum height of the shell , the time it takes
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Question 1031068: The height in feet of a fireworks shell can be modeled h(t) = -16t2+224t , where t is the time in seconds after it is fired.Find the maximum height of the shell , the time it takes to reach its maximum height , an the length of the time the shell is in the air Answer by solver91311(24713) (Show Source):
The graph of your function is a parabola. Since the lead coefficient is negative the parabola opens downward. Therefore, the value of the function at the vertex is a maximum. The value of the independent variable at the vertex of a parabola described by the function:
is given by
and the maximum value of the function is then
The total time of flight is the larger of the two roots of the equation formed by setting your function equal to zero. (zero assumes that the projectile lands at ground level rather than hitting some higher structure or going into a hole.
John
My calculator said it, I believe it, that settles it
