# Simple 2-D Projectile Motion Question

1. Sep 12, 2016

### Austin Chang

1. The problem statement, all variables and given/known data
A ball is thrown horizontally from the top of the cliff of height H. It hits the ground a distance H from the bottom of the cliff. What was the initial speed?

X coordinate
v0 = ?
a = 0 m/s2
x0 = 0
xf = H
Y coordinate
v0
a = -9.8 m/s2
y0 = H
yf = 0
2. Relevant equations
a(t) = a
v(t) = v0 + at
s(t) = x0 + v0t + 1/2*at2

3. The attempt at a solution
H = 0 + v0t
0 = H + 0 + 1/2 * (-9.8) t2
-H = 1/2*(-9.8)
H/4.9 = t2
(H/4.9)1/2 = t

2. Sep 13, 2016

### haruspex

Good so far. Why did you stop? You have two equations, each involving t. Do you expect to have t in the answer?

3. Sep 13, 2016

### hmmm27

Looks pretty confusing to me, but I'm new to this. You don't mind if i ask a few questions...

I don't see how the first and second equations are "relevant". (Actually I'm not entirely sure what the first equation is supposed to mean)

The third equation looks complicated.... should that be $d_t = d_{init} + v_{init}t + \frac {at^2}{2}$ ?

Yeah well, my first attempt ended up with the answer as $v=4.9t$

Last edited: Sep 13, 2016
4. Sep 13, 2016

### Austin Chang

Do i get H in my answer because I thought we were suppose to get a quantitative number

5. Sep 13, 2016

### Austin Chang

I just typed everything down on my page LOL, but answering your question the first and second question are me just integrating upwards because I dont like memorizing

6. Sep 13, 2016

### Austin Chang

and I got (4.9H)1/2 = v0

7. Sep 13, 2016

### PeroK

Can you see a reason why it must depend on H in this case?

If not, then trust your maths.

8. Sep 13, 2016

### hmmm27

which is what I got the second time I juggled the equations around.

Last edited: Sep 13, 2016
9. Sep 13, 2016

### Austin Chang

No because a question a while back asked if a ball is dropped from a certain height h and a ball thrown at a certain velocity hits each other in the middle with the same velocity. Find the height of h.
So I am confused because some questions you dont need height and others you do. Is this similar to the one variable one equation sort of thing

10. Sep 13, 2016

### hmmm27

It's up to the course you're taking and the teacher, what they want.

My take would be that the answer should be a speed (because it's explicitly stated, so duh) written as a function of H (because it already exists in the question, so using 't' would just be superfluous)

Last edited: Sep 13, 2016
11. Sep 13, 2016

### PeroK

Well, you just have to trust your maths. If you get a value for initial speed that depends on H, then that must be right.

In this case, it must depend on H.

12. Sep 13, 2016

### hmmm27

4.9t is also a "correct" answer.

His question is in what form should the answer be in, not what does random linear algebra produce.

Last edited: Sep 13, 2016
13. Sep 13, 2016

### haruspex

Dimensional analysis shows H must feature in the answer. You are only given H and g, a distance and an acceleration, and you are asked to find a velocity. You cannot find a velocity only given an acceleration since there is no way to disentangle the distance element of acceleration from the time-squared element. You would only be able to find other accelerations. But given a distance H and an acceleration g you can derive velocities of the form √(Hg).

Last edited: Sep 13, 2016
14. Sep 13, 2016

### haruspex

no it isn't. H was given in the question statement, so can validly be referenced in the answer. t was an unknown invented as part of the solution, so cannot appear in the answer. If that were allowed, you might just as well invent the unknown v for initial velocity and quote that as the answer!

15. Sep 13, 2016

### hmmm27

I often use quoties to indicate sarcasm or non-truth, among other things; in this case a "technical correctness".

Right, so what you said in your previous post, and what I said a few posts back, immediately after your post where you seemed (to me) to be promoting ambiguity in the answer. both of which earned us 'likes' from the OP who has gone away happy.

Last edited: Sep 13, 2016
16. Sep 13, 2016

### haruspex

It is no more correct, even technically, than answering v0. Anyway, please try to avoid posts which are likely to confuse students.
True, but not what you first posted.

17. Sep 13, 2016

### Austin Chang

Thanks guys both of you were really helpful. :P

18. Sep 13, 2016

### hmmm27

Betcha some of his class returned $4.9t$ as an answer, since that's the easiest algebraic route to take. And betcha they get part marks for it, too. So yes, it would be more correct than $v_0$

And I bet some people might think your "dimensional analysis" remark refers to nothing more meta than Cartesian coordinates.

Turned out the student had it right the first time but was confused by other solutions to similar problems. I was confused by his using the Relevant Equations section as a scratch pad, instead of cutting/pasting vanilla formulae from the textbook (which, through application of dimensional analysis I figger is what should go in there).

You Quoted a fresh post while I was editing it. I did actually hang around awhile, waiting for you to commit your comment. My bad for not getting it right the first time, but I don't recall there being any major differences pre/post-edit.

Last edited: Sep 13, 2016
19. Sep 13, 2016

### haruspex

I read it as saying that acceleration, in principle a function of time, is here a constant.
Not from me they wouldn't.
Eh?

20. Sep 14, 2016

### hmmm27

Well, that's how I read it too, but it didn't make sense in context of Relevant, since it's already a given from the "top of a mountain" parameter, and none of the other formulas allow for $a$ as a non-constant.

My kneejerk reaction is that a course that would require the student to map everything onto explicit x,y coordinates - when there's a perfectly reasonable simpler framework description("horizontal", "vertical") given that makes for a clearer solution and answer, gives part marks. Not an insult, just saying.

Okay, so what do you mean by "dimensional analysis" ?

Last edited: Sep 14, 2016