I need a formula for Height equals length of arc.

[SPiZ]

How do I find out what angle to fire a projectile so that the height it attains is equiv to the length of its arc? Whats a general formula? Assume the projectile is "fired" from ground level. Say, from a pea shooter or a sling shot.

 

[Fermat]

The projectile will travel in a parabola.

You use the eqns of motion to give eqns for movement in the x- and y-directions.
Eliminate t (time) from the two eqns to leave an eqn with y in terms of x, i.e. y=f(x) - which will be a parabola.

For the length of the curve look here.

 

[SPiZ]

Where would sin theta = cos theta? Wouldn't that give me the answer?

 

[Fermat]

Wait a minute. I've just realized what you're asking for.
It's never going to happen

By "length of arc", you did mean the length of it's path, S, yes ?

If you look at the attachment, The height attained, h, will never be equal to S.
The nearest it comes is when the projectile is fired straight up vertically, in which case you wiil get h = (1/2)S.
In all other cases h will be an even smaller fraction.

Did you copy down the question correctly ?

Where is this question from ?