Description

When you start the simulation, you will notice in the bottom part three separate 2D graphs ("Plotting Panel"):

Height Chart (y(t)): Shows how body height changes over time. Time (t) is on the horizontal axis, and height (y) on the vertical axis. In the first moments, the body rises, then at one point it stops at the maximum height H_max, and then it starts to fall. The shape of the parabola clearly indicates the deceleration during the ascent (due to the negative acceleration force) and the acceleration during the descent.
Velocity Graph (v(t)): This graph shows the instantaneous velocity of a body over time. At the beginning, when the body is thrown upwards, the velocity is positive and decreases until it reaches zero when it reaches H_max. After that, the velocity becomes negative (directed towards the earth) and increases in absolute value, because gravity accelerates the body downwards. The value v = 0 exactly marks the moment when the body stops climbing and starts falling.
Energy Diagram: On the third graph you will see two curves:
- Potential energy (E_p = m·g·y): increases as the body goes up (because y increases), and reaches a maximum when y = H_max. Then, as the body falls, E_p decreases.
- Kinetic energy (E_k = ½·m·v²): it is the highest at the moments when the speed of the body is maximum. At the very beginning E_k is ½·m·v₀². As the body decelerates during ascent, E_k decreases, to be zero at the moment v = 0 (at H_max). During the fall, v becomes negative but the square of the velocity increases, so E_k increases until the body reaches the ground again.

On the energy graph, you will notice that the sum of potential and kinetic energy is approximately constant (except for small numerical deviations), because the total mechanical energy in this ideal system (without air resistance) remains conserved:

E_uk = E_p + E_k ≃ constant

By looking at the velocity-energy diagram, it is easy to understand how energy is "switched" between kinetic and potential:

Rise: Kinetic energy is gradually converted into potential energy. Speed decreases, so E_k decreases, and height increases, so E_p increases.
At the top (H_max): Velocity is zero, E_k = 0, and all energy is potential (E_p = m·g·H_max).
Fall: Potential energy is converted back into kinetic energy. Altitude decreases, so E_p decreases, and speed increases in absolute value, so E_k increases.
Arriving on the ground: Potential energy is minimum (y = 0 ⇒ E_p = 0), and kinetic energy is maximum (v = –v₀ in the ideal case).

Use these graphs to track in detail how the energy changes throughout the simulation. This helps to visually understand the basic principle of conservation of energy and the parabolic motion of a vertical shot.