- #1

- 85

- 3

- Homework Statement
- A ball is thrown at an upward angle from an initial height 'h' above the ground. When the ball reaches a horizontal distance 'A' from the release point, it is at a maximum height 'H' above the ground. The ball eventually strikes the ground a horizontal distance 'R' from the release point. Assuming no drag, a horizontal ground, and a constant downward force of gravity (unknown), what is the height 'h' in which the ball was thrown in terms of 'H', 'A', and 'R'?

- Relevant Equations
- y_f=y_0+v_0 sinθt- 1/2 a_y t^2

x_f=x_0+v_0 cosθt

v_y=v_0 sinθ-a_y t

〖v_y〗^2=(v_0 sinθ)^2-a_y (y_f-y_0 )

This is not really a homework problem (it could be made to be though). I kind of made it up, inspired by a youtube math challenge problem involving parabolas, a water fountain where A = 1, R = 3, and H = 3. The solution given (h = 9/4) was based off simple math utilizing vertex form of a parabola. I wanted to find the problem just using kinematic equations. This is where I hit a roadblock (I assumed g was not necessary and treated it as an unknown). It took my a while (was dealing with 4 unknowns lol) but I eventually came up with the solution (using only kinematics). This is not normal as I'm able to do nearly all kinematic problem pretty quickly.

My question is : Would this be considered a simple problem (it wasn't for me)? If so then what technique would lead to a more elegant solution? Also, are there any solution methods involving the kinetic energy theorem?

I can post my complete solution (all steps) here if necessary. Just give the word.

For now the solution is

h = H [1 - {A/(R-A)}^2]

My question is : Would this be considered a simple problem (it wasn't for me)? If so then what technique would lead to a more elegant solution? Also, are there any solution methods involving the kinetic energy theorem?

I can post my complete solution (all steps) here if necessary. Just give the word.

For now the solution is

h = H [1 - {A/(R-A)}^2]