Bouncing ball

scorp007

Hi,

I'm trying to figure out how to calculate the resulting velocity vector of a ball after impact with a surface.

If the velocity vector is V {Vx, Vy, Vz} and The ball hits a surface with normal N {Nx, Ny, Nz} what would be the resulting vector of the new velocity?

Assuming the ball has an elasticity coefficient 0 <= k <= 1.

The angle of incidence won't be equal to the angle of reflection would it?

As an example V could be {0, -10, 0} and N {0, 1, 0}

Thanks.

HallsofIvy

Unless you are given some additional information, such as friction or that the ball is initially rotating, yes, the angle of reflection will equal the angle of incidence. In the example you give, the ball is striking the surface perpendicularly so even with friction, unless it is rotating it will bounce straight up. The only thing you need to calclulate is the y component of velocity.

Saying "the ball has an elasticity coefficient 0 <= k <= 1." means that the total energy after the bounce will be k times the total energy before the bounce. I assume the V given is the velocity just before bouncing and you want the V just after bouncing so the potential energy is the same at each time and you can take that to be 0. You only need to look at the kinetic energy. What is the kinetic energy of a ball of mass m with V= (0, -10, 0)? What is the velocity of a ball, going upward, of mass m with kinetic energy k times that?

scorp007

Thanks for the reply.

Lets ignore the friction and rotation for now.
Assuming the mass is 1kg.

Ek = 1/2 * m * v^2 =
1/2 * 1 * (sqrt(0^2 + (-10)^2 + 0^2))^2 =
1/2 * 100 = 50.

Not too sure how the kinetic energy fits into the equation...

In this case, yes just the y component, but this was only a simple example.

Wouldn't the resulting velocity vector V be k * {0, 10, 0} (incident velocity reflected)?