I just did a basic projectile motion experiment. What I did was build a small catapult out of small Popsicle sticks and rubber bands, and then I used it to launch a small ball at an angle above the ground. I wanted to figure out the total potential energy of the catapult when I pulled it back to launch the ball.
To do this, I figured that I should find the ball's total energy in both the x- and y- axis (ignoring anything in the z-axis). For the x-axis, I figured out the ball's horizontal Ek by dividing the horizontal distance it traveled by the time it took. This gave me the ball's horizontal speed, which I used to find its Ek. Due to the conservation of energy, I reasoned that the ball's energy in the x-axis must have been this value for the entire time (there were no horizontal forces acting on the ball, ignoring drag).
For the y-axis, I measured the distance above the ground that its highest point of flight was. Then I figured out the GPE at the highest point by using this value. Once again, I reasoned that the ball's energy at all times in the y-axis was this value, due to the conservation of energy (once again, ignoring drag).
At this point, I had the ball's energy in the x- axis and y-axis. To find the ball's total energy, I just added up both of the values. This told me how much potential energy was in the catapult when it was drawn back.
I was wondering if my steps were correct. Was what I did with adding up the energy in the x- and y- axis to find the total energy correct? I figured this was allowed since energy is a scalar, so direction shouldn't matter.