Parabola question

Factual Questions
1

Ok, the problem is: A ball is trhown upward and outard from the top edge of a 50 foot tall building. When it is 10 feet from the building it reaches its greatest height of 20 feet above the buildings edge. When the ball hits the ground, how far is it from the base of the building. My daughter and I got different answers. I solved it thusly:

Vertex is 0,70
Known points are -10,50 and 10,50

h=0, k=70
solve for a gives (50-70)=a(0-10)squared
a=-1/5

Solve for x at ground level:

(0-70)=-1/5(x-0) squared
350=x squared
x=5*sqrt14 + 10

I won’t bother with her answer. If mine is wrong, I will assume hers is right.

2

Break it down into x (parallel to ground) and z (orthogonal to ground) coordinates.

How long does it take to fall 70 feet (z)? Free fall, no friction.

How far (vt) does it travel in the x direction in that time?

Add that to 10 feet. That the answer.

3

I’m sure that would work, but this part of the book just deals with formulae for parabolas and such and therefore the answer will lie in solving said formula. I had to study up just to help her with this problem and don’t really want to delve back into vectors.

4

dauerbach: I get the same answer you do.

John Mace: It’s much simpler to just look at the equation of the resulting parabola. Breaking it down into horizontal and vertical motion requires you to introduce time, which is really extraneous here. (Not to mention having to assume a particular acceleration due to gravity.) Conceptually nice, but big time overkill for this problem.

5

Topo:

Explain how you solve this w/o knowing g. The answer would be different on the moon, no? g determines the shape of the parabola.

6

Yes, but so does v[sub]0[/sub]. You could get an identical shape on the moon by varying the initial speed.

7

John Mace Yes, gravity does determine the shape of the parabola, in the ultimate and physics-y sense of the word. But in terms of the math, knowing one point and the vertex defines a parabola (in the sense that there is only one parabola that fits those two points) and since they are given, you don’t need to assume anything about gravity.

If you were given only the initial position and velocity, then you would need to use g to figure out the landing spot.

8

John Mace Yes, gravity does determine the shape of the parabola, in the ultimate and physics-y sense of the word. But in terms of the math, knowing one point and the vertex defines a parabola (in the sense that there is only one parabola that fits those two points) and since they are given, you don’t need to assume anything about gravity.

If you were given only the initial position and velocity, then you would need to use g to figure out the landing spot.

But the answer to this problem, as stated, is independent of gravity; in order to have the ball top out 20 feet up and 10 feet out, you’d have to throw it a heck of a lot less hard on the moon than on the earth, but if you did, it would land in the same spot (neglecting, of course, air friction and all that), having taken a lot longer time-wise to fall, but having also been given far less horizontal velocity at the outset.

9

Got it. Didn’t pay attention to the vertex thing.

10

Thanks topo, she thinks she is always right. Glad to hear I was correct for once.

11

Didn’t get back to check on this thread until now. Thanks Achernar and viking for supplying the further explanations. I tend to be a lurker unless it’s something I really know about; it’s nice to be able to pitch in every now and then.

I hadn’t thought of “topo” as a nickname, but I kind of like it.