Energy With Projectile Motion

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.

• Energy is not a vector. It does not have components. (Occasionally you find cases where you can treat it as if it did, but those are the exception, and you have to understand how energy works as a scalar to be able to identify them. However, this is not such a case.) – dmckee Apr 15 '17 at 1:05
• Thanks. I wasn't really thinking of energy as having components, it was just a way for me to work with it easier. Was my method or finding total energy correct? – Inertial Ignorance Apr 15 '17 at 1:37
• You can find the launch speed from the maximum range, without any need to measure time of flight. – sammy gerbil Apr 15 '17 at 4:33
• Isn't it necessary to measure the time the projectile took to reach that distance though? Since speed = distance / time. – Inertial Ignorance Apr 15 '17 at 5:10

Talking about kinetic energy along the x- or y-axis is not quite correct, but close enough if you calculate it explicitly like this: $$K = \frac{1}{2}mv^2 = \frac{1}{2}m(v_x^2 + v_y^2) = \frac{1}{2}mv_x^2 + \frac{1}{2}mv_y^2$$