Question

An archer releases an arrow from a shoulder height of 1.39 m. When
the arrow hits the target 18 m away, it hits point A. When the target is
removed, the arrow lands 45 m away. Find the maximum height of the
arrow along its parabolic path.

Answer 1

@satellite73 Can you help me with this question?

Answer 2

the parabola is defined by the equation:

y = f(x) = ax² + bx + c

...where a, b, and c are constant coefficients to be determined. You are given three points:

f(0) = 1.39
f(18) = h ... (height of point A) ... I suspect there's a figure you're not showing us
f(45) = 0

Answer 3

You need that height h to solve the problem.

Answer 4

That will give you three equations in 3 unknowns

Answer 5

Oh, the height is suppose to be 5 feet.

Answer 6

When you get a value for h, you can solve for a and b. If a is not negative, you have a problem since a trajectory should always be a parabola that opens downward. The maximum height will be where x = -b/(2a)

Answer 7

okay, i am confused.

Answer 8

Till Where Did You Really Get It ?

Answer 9

Well, I understand the equation, not really when you labeled the points.
"f(0) = 1.39
f(18) = h ... (height of point A) ... I suspect there's a figure you're not showing us
f(45) = 0"

Answer 10

@hba

Answer 11

Okay So Let Me Continue From Here :)

Answer 12

You need that height h to solve the problem. That will give you three equations in 3 unknowns:

a(0²) + b(0) + c = 1.39 .
a(18²) + b(18) + c = h
a(45²) + b(45) + c = 0

You can simplify that to two equations, since c=1.39 is known:
324a + 18b = h - 1.39
2025a + 45b = -1.39

Answer 13

ax² + bx + c ^^

Answer 14

You Get It ? @TiffanyLee3

Answer 15

yea, a little, I was just reading over it

Answer 16

When you get a value for h, you can solve for a and b. If a is not negative, you have a problem since a trajectory should always be a parabola that opens downward. The maximum height will be where x = -b/(2a)

Answer 17

I have no idea where to even start with that..

Answer 18

Its f(x)=ax^2+bx+c=0

Answer 19

Then what do i do with all of this
f(-b/(2a)) = a(-b/(2a))² + b(-b/(2a)) + c
= b²/(4a) - b²/(2a) + c = c - b²/(4a)

Answer 20

Jus Plug in x= -b/2a

Answer 21

I Am Really Sorry But I Have To Leave

Answer 22

I hope You Understood ?

Answer 23

Nope, not really, Ill just leave this one blank

Answer 24

No Answer It

Answer 25

I do not know how.

Answer 26

Someone else answered the same question earlier. The solution is attached below.

All credits to Phi, I take no credit whatsoever. Just restating the answer where it's needed.