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- Thread starter Binaryburst
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- #2

tiny-tim

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Hi Binaryburst! Welcome to PF!

Start by using conservation of energy, and that will give you v as a function of y.

Carry on from there.

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- #4

tiny-tim

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you now have x' as a function of x (or y' as a function of y)

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I'm on it.

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I get elliptic integral !?

- #7

tiny-tim

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very likely!

well, if you *will* start with a *parabola!*

- #8

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Wow... Thanks a lot! :D this is great!

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If I take the whole speed, not just it's components I get a sin(t) :D

- #10

tiny-tim

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sorry, not following you …

you'll need to show the equations

- #11

rollingstein

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I was trying too. Do you get:I get elliptic integral !?

dx/dt=sqrt(2g) sqrt((1-4*x^2)*(x1^2-x^2))

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Nope. I'll post the equations right away.

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I get this: (2g(x1^2-x^2))^0.5. Then if i integrate it with respect to t i get x=x0*sin(t(2g)^0.5).

- #14

rollingstein

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I get this: (2g(x1^2-x^2))^0.5. Then if i integrate it with respect to t i get x=x0*sin(t(2g)^0.5).

Somehow my expression for v_x has an additional (1-4x)^0.5 factor. Not sure what I'm doing wrong.

- #15

rollingstein

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This term (2g(x1^2-x^2))^0.5I get this: (2g(x1^2-x^2))^0.5. Then if i integrate it with respect to t i get x=x0*sin(t(2g)^0.5).

Is that your v or v_x?

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My equation is for v alone.

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I'm thinking how could i get it without using the conservation of energy and using forces.

- #18

rollingstein

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What did you do next?My equation is for v alone.

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Int( 1/f(x)* dx/dt * dt ) = int( 1 dt )

- #20

rollingstein

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That's where I think you are wrong.

Int( 1/f(x)* dx/dt * dt ) = int( 1 dt )

You've put v=dx/dt.

Only v_x = dx/dt

But I could be talking nonsense! Be warned. But I'd love to see your opinion.

Your solution does look super tempting! :)

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- #22

rollingstein

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Funny point is your solution seems to satisfy all the boundary conditions etc. I'm puzzled.Hmmm.. That's interesting I actually got the vx. Sorry for the blunder. I was too excited :)

My solution integrates to something super messy. :(

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I am super puzzelled as well. I can't figure out what I did.

- #24

rollingstein

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Another reason why your solution seems wrong to me.

take dx/dt and dy/dt

[itex]v_x^2 + v_y^2 = v^2 [/itex]

But yours don't seem to sum up to v. Try.

take dx/dt and dy/dt

[itex]v_x^2 + v_y^2 = v^2 [/itex]

But yours don't seem to sum up to v. Try.

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