SOLUTION: an arrow is fired into the air with an initial velocity of 160 feet per second. The height in feet of the arrow t seconds after it was shot into the air is given by the function h
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Question 608152: an arrow is fired into the air with an initial velocity of 160 feet per second. The height in feet of the arrow t seconds after it was shot into the air is given by the function h(t)= -16t^2+160t. find the maximum height of the arrow.
Found 2 solutions by Alan3354, solver91311:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
an arrow is fired into the air with an initial velocity of 160 feet per second. The height in feet of the arrow t seconds after it was shot into the air is given by the function h(t)= -16t^2+160t. find the maximum height of the arrow.
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The simplest way to do this is to find the 2 times when h = 0, at launch and at impact.
The time at max height is the average of the 2, or 1/2 the total time of flight.
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-16t^2+160t = 0
t = 0 (launch)
t = 10 (impact)
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h(t)= -16t^2+160t
Max ht is h(5)
= 400 feet
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
Well, not exactly.
Your height function ignores the initial height of the tip of the arrow at the time of release. This value is other than zero unless the archer is standing in a hole of sufficient depth such that the tip of the arrow is exactly at ground level at the time it is released.
\ =\ -16t^2\ +\ 160t\ +\ h_o)
Where 
is the initial height. We'll just accept the "archer in a hole" scenario for the time being and assume that 
.
The graph of your function is a parabola. Because of the negative lead coefficient, the parabola opens downward, meaning that the vertex is a maximum value of the function. The 
coordinate of the vertex of a parabola described by the function \ =\ ax^2\ +\ bx\ +\ c)
such as this one is given by:
Calculate 
Once you have a value for the coordinate of the vertex, calculate
)
to get the value of the function at the vertex, i.e. the maximum value of the height function. If you decide later that is actually something other than zero, you can just add it on at the end.
John
My calculator said it, I believe it, that settles it
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