# Finding the angle

1. Sep 23, 2015

### astrololo

1. The problem statement, all variables and given/known data

A fountain projects water horizontaly at a height of 12 m. The water goes on the floor after having travelled 15 m horizontally. Calculate the angle the water does with the floor.
2. Relevant equations
I know that the accelerate is constant, so its one of the cinematic equation. Not sure of which one.

3. The attempt at a solution

I have no idea on how to do this. I know that I must decompose my situation in to two components, one for the x's and the other for the y's. Any hint would be helpful !

2. Sep 23, 2015

### Staff: Mentor

You could approach the problem via kinematic equations, but that may be the long way around.

Consider what type of curve a projectile describes. If you can find an equation to fit your given data then you should be able to find the slope (hence the angle) at any point along the curve...

3. Sep 23, 2015

### astrololo

Vx^2 = Vx initial^2 + 2a(x-xinitial) ??? I know that its a parabola

4. Sep 23, 2015

### astrololo

5. Sep 23, 2015

### Staff: Mentor

Okay, ignoring the kinematic view for the moment, and thinking in terms of functions from math class, let's start with a general expression for a parabola that would suit the given situation:

y(x) = ???

6. Sep 23, 2015

### astrololo

y=-x^2+c

7. Sep 23, 2015

### Staff: Mentor

Close. You need to add a coefficient to the $x^2$ term to account for the "width" of the parabola. The "c" term takes care of the vertical offset. So write:
$$y = -a x^2 + c$$
Can you find a and c using the known data points?

8. Sep 23, 2015

### astrololo

12 and 15

9. Sep 23, 2015

### Staff: Mentor

Justify.

10. Sep 23, 2015

### astrololo

Oh I actually have (0,12) : (15,0) Which I can use I think. to find the general equation.

11. Sep 23, 2015

### astrololo

ok i found y=-4/75x^2 + 12

12. Sep 23, 2015

### Staff: Mentor

Excellent. Now can you find the angle where it meets the "floor"? Think: slope, tangent,...

13. Sep 23, 2015

### astrololo

Are you suggesting that Ishould use differential calculus ?

14. Sep 23, 2015

### Staff: Mentor

Unless you can dig up a "canned formula" for the slope of a parabola from your Functions class notes, I'd suggest calculus, yes.

15. Sep 23, 2015

### astrololo

Then this isn't the right way to do it. I know calculus, but I'm not supposed to use it now.

16. Sep 23, 2015

### Staff: Mentor

Ah. That's a shame, because the work is essentially done

So I guess it's back to kinematics then. I suggest you start by finding the vertical velocity at impact, and the time to impact. You can do this because you know that the vertical and horizontal components can be treated separately, and you know the distance and acceleration involved.

Last edited: Sep 23, 2015