book, read, student @ Pixabay

The path of a model rocket can be modelled using the following equation:

x = h-sin(theta) y=0.5*h-cos(theta) z=-10+sqrt((2^3)*g*h)/9.81, where (x, y, z) is in meters and time t is in seconds. The vertical component of velocity decreases exponentially with height while the horizontal component remains constant at zero until reaching maximum altitude.

v2 rocket, ariane 5 launcher, rockets in the size comparison @ Pixabay

The height of the model rocket when it reaches maximum altitude can be found using this equation:

h=sqrt((x^*)/g) h is in meters and x is in meters. After reaching its apogee, a model rocket will fall back to earth at a rate that’s proportional to time squared (in seconds). This means that twice the amount of time after liftoff will result in four times as much distance fell.

For example, if t equals 100 seconds, one-quarter of the way down from max altitude, we’ll have travelled about 150 m away from our launch point while travelling 150 m/s vertically downward. The total energy available for an object on Earth comes from gravity or electrical potential.


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