Projectile Mechanics: Find Distance from h & R

[Billybob]

Homework Statement

A project is fired from an origin that reaches a height (h) and range (R). Show y = (4h/r)x (1-x/R). Then find the distance.

Homework Equations

Any really. I was just using h(max) = v[y]t+1/2at^2, then R=v[x]t, then trying to put them both into y=mx+b... but nothing really comes of it.

The Attempt at a Solution

I managed to solve for V[y] to be (-gt) then for V[x] to be R/T... then I eventually worked it to y=(x/R)(h+ (v^2/4h)t^2... but can't seem to find anything for T or really get any closer...

Thanks...

 

[Jhero]

Hello there,

It seems like you have made some progress in your solution, but there are a few things that need to be clarified in order to fully solve the problem. First, what is the initial velocity of the project? This is necessary in order to find the equations for V[y] and V[x]. Additionally, it would be helpful to know what the initial height (h) and range (R) are, as these values will also affect the final equation.

Once you have all of these values, you can use the equations you mentioned (h(max) = V[y]t+1/2at^2 and R=V[x]t) to find a relationship between time and distance. From there, you can substitute this relationship into the equation y = (4h/r)x (1-x/R) and solve for the distance.

I hope this helps and good luck with your project!