Calculating Velocity Vector after Ball Impact with a Surface

In summary, if the velocity vector is V {Vx, Vy, Vz} and the ball hits a surface with normal N {Nx, Ny, Nz}, the resulting vector of the new velocity would be V {-10, 0, 10}.
  • #1
scorp007
5
0
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? :confused:

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

Thanks.
 
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  • #2
scorp007 said:
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? :confused:

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

Thanks.
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?
 
  • #3
HallsofIvy said:
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?

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... :redface:

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)?
 

1. What is velocity vector and how is it calculated?

Velocity vector is a mathematical representation of an object's speed and direction of motion. It is calculated by dividing the change in position by the change in time.

2. How does the surface impact affect the velocity vector of a ball?

The surface impact affects the velocity vector of a ball by changing its speed and direction of motion. This is due to the forces exerted on the ball during the impact, such as friction and gravity.

3. What factors influence the calculation of velocity vector after ball impact with a surface?

The factors that influence the calculation of velocity vector after ball impact with a surface include the mass and velocity of the ball, the angle of impact, the type and condition of the surface, and the presence of any external forces.

4. Can the velocity vector after ball impact be predicted?

Yes, the velocity vector after ball impact can be predicted using mathematical equations and physical principles, as long as the factors that influence the calculation are known.

5. How is the velocity vector after ball impact with a surface used in real-world applications?

The velocity vector after ball impact with a surface is used in various real-world applications, such as sports science and engineering, to analyze and improve the performance of athletes and equipment. It is also used in accident reconstruction to determine the speed and direction of objects involved in collisions.

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