Question

"An archer releases an arrow from a shoulder height of 1.30m. When the arrow hits the target 18m away, it hits point A. When the target is removed, the arrow lands 45m away. Find the maximum height of the arrow along its parabolic path." (Will post target picture.) Would greatly appreciate help and possible explanation!! :)

Answer 1

you are given 3 points of reference .... develop a system of 3 equations

Answer 2

or, there are other methods

Answer 3

and also, this is an old question that has a picture in order to determine the height of point A on the target

Answer 4

one of newtons methods is simply to build up on the points.

given some reference points: (xo,yo) (x1,y1) (x2,y2)

we can construct an equation that zeroes out everything else to focus on one part at a time

y = a + b (x-xo) + c (x-xo)(x-x1)

when x=xo, y=yo

yo = a + b (xo-xo) + c (xo-xo)(xo-x1)
yo = a + b (0) + c (0)
yo = a




when x=x1, y=y1

y1 = a + b (x1-xo) + c (x1-xo)(x1-x1)
y1 = a + b (x1-xo) + c (0)
y1 = a + b (x1-xo)
(y1-a)/(x1-xo) = b




when x=x2, y=y2

y2 = a + b (x2-xo) + c (x2-xo)(x2-x1)

y2 - a - b (x2-xo) = c (x2-xo)(x2-x1)


y2 - a - b (x2-xo)
--------------- = c
(x2-xo)(x2-x1)

Answer 5

but the system of 3 equation works just as well: given a parabola ax^2 + bx + c = y

(xo)^2 a + (xo) b + c = yo
(x1)^2 a + (x1) b + c = y1
(x2)^2 a + (x2) b + c = y2

and we can then solve for abc using whatever approach works best for you

Answer 6

I still do not understand what you are trying to explain..

Answer 7

well, at this point, you should be bale to know how to work systems of equations. what do you know about them?

Answer 8

it also appears that you do not have a workable reference for the point A .... the height of the stand would be needed to define a static point