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Equations


With an understanding of the basic functions of a catapult, one can use the following formulas to ascertain measurements pertaining to its operation.




First, one can calculate the stored energy in the system when the catapult arm is held back:

k = elastic constant
x = distance pulled back
  • Kinetic energy of the catapult upon release: ( k ) x² / 2 
  • if the elastic band is looped, this value must be doubled


Next, one can calculate the trajectory of the launch:

v = angle created with arm when it is pulled back
g = gravitational constant
  • Height = ( v sinθ )² / 2g
  • Time of flight = 2 v sinθ / g
  • Range or horizontal distance covered = v² ( sin 2θ ) / g
  • assumes zero loss


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