Bounce a ball from one point to another - Vector and Acceleration

Question

I have a ball which drops to a point, from which it should bounce and reach another point.

My ball starts with an acceleration towards the first point, hits the point and bounces off to the left side. What I want is the velocity & acceleration applied to the ball after hitting the first point, so it both has a bouncing effect, and reaches it's destination (doesn't go offside, like the bright trail).

I have the linear vector between points, coordinates of points and angle between them.

Explanation

What's your question? Where's your code? What have you tried? — j08691, Jun 13 '15 at 15:49
some similar questions worth looking: [cannon ball trajectory](http://stackoverflow.com/a/26174961/2521214) , [Bouncing Ball](http://stackoverflow.com/a/20017455/2521214) — Spektre, Jun 14 '15 at 08:33

score 2 · Answer 1 · answered Jun 13 '15 at 16:06

2

First we figure out how long it will take to get from the higher point to the lower point by solving for t:

at² + v_iyt = dy

Then we take t and use it for our lateral velocity:

v_x = dx / t

Once you have the lateral velocity, just slice time up as finely as you like and move the ball to each calculated point in turn.

answered Jun 13 '15 at 16:06

Ignacio Vazquez-Abrams

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Could you please add some details on the math? I don't get what a in at² and the indices on v mean. I would like to try it. – stacker Jun 13 '15 at 20:00
@stacker `a.t^2+v(iy)=dy` is y axis equation of the bounced movement `a` is local forcefield (gravity) acceleration (usually `-9.81m.s^-2`), `v(iy)` is the incident speed in y axis after hitting the ground the first time, `t` is time from the first bounce and `dy` is the ground line size in y axis only `a,v,dy` are knowns `t` is unknown you need to solve that quadratic equation and the resulting positive `t` is time the ball need to hit the second bounce point .the rest should be clear ... – Spektre Jun 14 '15 at 08:22

score 0 · Answer 2 · edited May 23 '17 at 12:30

If you don't want a full blown physics simulation you could fake this by a linear interpolation (lerp) from the start point to end-point.

See Moving object from vector A to B in 2d environment with in increments of percents for lerp in java script.

Change the coordinate pointing upwards (y or z) depending on the coordinate system you use. While t is animated from 0..1:

 var relativeHeight = Math.Sin( t * Math.PI ) * curveAmplitude;
 posy = orgPosy + relativeHeight;

Bounce a ball from one point to another - Vector and Acceleration

2 Answers2