Calculating Velocity at a Specific Point on a Curved Slit

[Melawrghk]

Homework Statement

The shape of the arch is defined by a sine function with a = 0.2 and the width of the arch is 1m. The velocity v is constant at 2m/s. What is the velocity at point P when x=0.25m?

The Attempt at a Solution

So since v is just in the x-direction, I figured that's the v_x speed.
Then I came to having to find an equation to v_y and this is where I get stuck. I remember from high school physics that equation of velocity can be essentially found by taking a derivative of the position equation.

In this case I get:
v_y=y'=0.2*pi*cos(pi*x)

From which I can find that at x=0.25m, v_y = 0.444288 m/s
But that combined with the horizontal speed of 2m/s gives me a resultant velocity of 2.05ish, instead of 2.19 that I'm supposed to get. Help please?

 

[turin]

It is asking for acceleration, not velocity. You are adding apples to oranges.

BTW, is that the exact wording of the problem? - it is appauling.

 

[Melawrghk]

Yeah, that's the exact wording.

Sorry, the question is a two parter. I'll fix that. I just decided to not even tackle acceleration if I can't figure out velocity.

 

[turin]

Where did I see acceleration?! I must be going mad. I am so sorry. Anyway, your velocity calculation is almost correct. Your problem is that vy is the derivative of y wrt t, not x. Think chain rule.

 

[Melawrghk]

Oh thank you, thank you! :) That allows me to get acceleration as well. Yay!

 

[Melawrghk]

Except... Now I'm doing a question that's basically the same, except

y=0.23sin(pi*x) and Vx=2.4m/s and we have to find velocity at x=0.32

I did the same thing as before and got:
Vy = 0.552*pi*cos(2.4*pi*t)

But the thing in the brackets ends up being >1 and that can't be. What did I do? :S

 

[turin]

Vy = 0.552*pi*cos(2.4*pi*t)

But the thing in the brackets ends up being >1 and that can't be. What did I do? :S

What thing in brackets? Do you mean 2.4πt? What's wrong with that being >1?

 

[Melawrghk]

Yes that, but cos can't be >1...

 

[turin]

The cosine is not >1; its argument is >1. The domain of cos(x) is x any real number, (and actually this can be generalized even further). I think you're worried about the range. Don't worry about that; your calculator will take care of it.