Question

I'm doing a project in algebra and I want to make sure I'm doing it right... Activity one says... Measure the distance from the fl oor to your shoulder when you are standing.
Suppose you release an arrow and it hits the target at a point 5 ft above the
ground. Sketch a possible parabolic path of your arrow’s flight using this
information.
Help asap please.

Answer 1

to sketch a parabola, you should start with 3 points
the starting point at x=0 (horizontal distance) and y= should height (vertical distance)
the end point is x = how far away the target is and y = 5 ft (height of the target)
then pick a point halfway, and a little bit above both the shoulder height and 5 ft
sketch in the curve.

Answer 2

Okay, so where would I put the point of my height??? @phi

Answer 3

let's say your should is at 5 feet
then the starting point for the arrow is at (0,5)

Answer 4

*shoulder

Answer 5

okay, so since to my shoulder it's 4,7 would the point be (4,7)
@phi

Answer 6

what is 4,7 ?

4 feet 7 inches ?

if so , change it to 4+7/12 = 4.6 feet

the starting point is (0, 4.6)
(the x is always 0... the y is the height of the shoulder in feet)

Answer 7

Okay! & the next point would be (0,5)

Answer 8

the x number is the distance going sideways.
If you are at the start line (call this x=0)
then the arrow hits the target at some x bigger than 0 (if you use x=0, the arrow is still at the start)

Answer 9

Okay, so what would I do??

Answer 10

the x for the target is how far away the target is (in feet)
pick a nice number but not a goofy number like 3 (too close)

Answer 11

2???

Answer 12

Have you ever seen robin hood shooting an arrow. Does he shoot that things 2 feet in front of him?

Answer 13

Hahah , no . Okay .. What about 10 ?

Answer 14

okay, but that is still pretty close. But at least you can do that.

Answer 15

so my point would be (10,5)

Answer 16

yes.

now half way between (that would be at x=5) pick a height a little above 5
because a parabola as an arc to it (it has to go up and then down)

Answer 17

8 ?

Answer 18

@phi

Answer 19

you could, but I would use these numbers:
(0,4.6), (20, 5.5), (40,5)

now plot those 3 points, and draw a curve through them.

Answer 20

Alrighty. Give me a second. I'm gonna attach a picture of my graph when I'm finished.
@phi

Answer 21

and when you are done, you can watch robin hood shooting
https://www.youtube.com/watch?v=n3hDAaxHNjs

Answer 22

LMAO!!

Answer 23

for the 3rd point can i do (38,5)??

Answer 24

yes, that is ok

Answer 25

This doesn't look right @phi

Answer 26

@phi

Answer 27

the parabola goes through the 3 points, but it does not "turn down".
It is very flat. Like this

Answer 28

so like this @phi

Answer 29

yes. that looks good.
btw, here is what the parabola looks like if we zoom out
you see that the arrow is just a very short part at the very top of the curve

Answer 30

Ohhh! Okay, I get it. So, that's how I do this?? I'm done with this one??

Answer 31

yes, you are done for this part.
Are they going to ask you to find the equation for this parabola ?

Answer 32

No, I have to do another sketch like this, but sitting down... and then I have to state differences and similarities in the two... Could you help me with the second sketch??

Answer 33

sitting down changes the first point to (0, 3) (for example)
in other words, the height will be less at the start

Answer 34

to my shoulder it's 3 ft 4 in

Answer 35

change that to 3 + 4/12 = 3.3 feet

Answer 36

so (0,3.3)

Answer 37

(it's 3.3333 feet, but we should round to 3.3 feet)

Answer 38

yes, (0,3.3)

Answer 39

would the other points be the same

Answer 40

Yes, we could leave them the same. Definitely the last point stays the same (that is where the target is)

Answer 41

ok one second

Answer 42

@phi

Answer 43

yes. looks good.

Answer 44

How would I even start to explain similarites and differences?

Answer 45

you would start by listing what is the same about them.
then you would list what is different.

Answer 46

There's nothing different accept my height...

Answer 47

the starting height is different.

what about the shape ?

Answer 48

The first sketch is more of a straight line, whereas the second sketch has more of a curve?

Answer 49

yes.

also, an important point of a parabola is where it peaks (i.e. the vertex)
it looks like the first parabola has a vertex close to the middle between you and the target.
the vertex in the 2nd parabola is closer to the target.

Answer 50

that sounds like most of the differences

Answer 51

Alrighty! Thank you so much!! :)

Answer 52

I assume you can list how they are the same?
they both make an arc (though one is flatter than the other)
they both go to the same end point (the target)

Answer 53

Yes!:)