How exactly can I calculate time until a ball fall if I know initial and final x and y position of a ball, gravity, delta time, initial dx and dy of a ball and its speed calculated from the formula sqrt(dx ** 2 + dy ** 2)?

  • \$\begingroup\$ Which level of precision do you need? E.g. If you want to simulate a tenis ball with rotation/effects or just a simple, ball without atmosphere? \$\endgroup\$ Nov 16, 2016 at 12:02
  • \$\begingroup\$ I want to simulate a small ball with no effects, without atmosphere. This equation should provide also horizontal motion, not only free fall with dx = 0 \$\endgroup\$
    – Tkininter
    Nov 16, 2016 at 12:23
  • \$\begingroup\$ Downvoted as OP obviously did not make a lot of research before posting... \$\endgroup\$ Nov 16, 2016 at 12:28

2 Answers 2


Supposing a macroscopic ball falling without atmosphere resistance and where Relativist effect is negligible.

  • P0[x,y,z] is the initial position of the ball, with y >= r
  • P[x,y,z] is the final position of the ball.
  • V0[x,y,z] is the initial speed of the ball
  • g[0,y,0] is the gravity, with y < 0
  • r is the radius of the ball, r >= 0
  • ground is defined as a plane at Y=0

The position of the ball at any moment is given by (1):

P = P0 + V0*t + g*t*t;

To found the time where the ball hit the ground (2):

P0.y + V0.y*t + g.y*t*t = r

Solving the equation (3):

t = ( -V0.y - sqrt(V0.y*V0.y - 4*g.y*(P0.y-r)) ) / (2 * g.y)

Final position can be calculated using (1)

Note: Considering that P0.y >=r and g.y is negative, the internal of the root is always positive.


an unusual answer cause its mostly a link, but this is the way to calculate object falling according to X gravity following newton's law.



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