- #1

h1a8

- 87

- 4

- 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]