Two particles with masses 2m and 9m are moving toward each other along the x axis with the same initial speeds vi. particle 2m is traveling to the left, while particle 9m is traveling to the right. they undergo an elastic, glancing collision such that particle 2m is moving in the negative y direction after the collision at a right angle from its initial direction. (a) find the final speeds of the two particles in terms of vi. particle 2m ✕ vi particle 9m ✕ vi (b) what is the angle θ at which the particle 9m is scattered? °

The final speed for the mass 2m is and the final speed for the mass 9m is .

The angle at which the particle 9m is scattered is with respect to the - y axis.

Explanation:

In an elastic collision the total linear momentum and the total kinetic energy is conserved.

Conservation of linear momentum:

Because the linear momentum is a vector quantity we consider the conservation of the components of momentum in the x and y axis.

The subindex 1 will refer to the particle 9m and the subindex 2 will refer to the particle 2m

In the x axis before the collision we have

and after the collision we have that

In the y axis before the collision

after the collision we have that

so

then

Conservation of kinetic energy:

so

Putting in one side of the equation each speed we get

We know that the particle 2m travels in the -y axis because it was stated in the question.

Now we can get the y component of the  speed of the 9m particle:

the magnitude of the final speed of the particle 9m is

The tangent that the speed of the particle 9m makes with the -y axis is

As a vector the speed of the particle 9m is:

As a vector the speed of the particle 2m is:

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