How Do You Calculate Final Velocities in a Two-Mass Elastic Collision?

[davev]

http://i.minus.com/i7YDkagp0bChQ.png

Homework Equations

p = mv

(v1m1 + v2m2)
Vf = --------------------
(m1+m2)

The Attempt at a Solution

I got that the total momentum was 9.64 by using p=mv for summing m1, v1 and m2, v2. Then I used inverse trig to try to find the angle, but all the answers I submit are incorrect. I'm not sure what way to go here.

 

[ehild]

The momentum is vector, and the momentums sum as vectors.

ehild

 

[davev]

All the answers are still positive, so I don't understand what you mean.

 

[ehild]

How do you add two vectors?

ehild

 

[Nickie]

The collision shown in the image appears to be an elastic collision, where both masses retain their original shape and total kinetic energy is conserved. In this case, we can use the equation for conservation of momentum, which states that the total momentum before the collision is equal to the total momentum after the collision.

In this case, we can write the equation as:

m1v1i + m2v2i = m1v1f + m2v2f

Where m1 and m2 are the masses of the two objects, v1i and v2i are their initial velocities, and v1f and v2f are their final velocities after the collision.

We are given the initial velocities of both objects (v1i = 5.2 m/s and v2i = 3.8 m/s) and we can calculate their masses from the given information (m1 = 1.8 kg and m2 = 1.4 kg). So we have:

(1.8 kg)(5.2 m/s) + (1.4 kg)(3.8 m/s) = (1.8 kg)(v1f) + (1.4 kg)(v2f)

Solving for v1f and v2f, we get:

v1f = (1.8 kg)(5.2 m/s) + (1.4 kg)(3.8 m/s) - (1.4 kg)(3.8 m/s) / 1.8 kg = 4.6 m/s

v2f = (1.8 kg)(5.2 m/s) + (1.4 kg)(3.8 m/s) - (1.8 kg)(5.2 m/s) / 1.4 kg = 4.4 m/s

So after the collision, the first mass will be moving at 4.6 m/s and the second mass will be moving at 4.4 m/s. To find the angle of the final velocity vector, we can use the equation:

Vf = √(vxf^2 + vyf^2)

Where vxf and vyf are the x and y components of the final velocity vector. Since the collision is in one dimension (x direction), the final velocity vector will only have an x component. So we can write:

Vf = √(vxf^2)

Where