A 100 g ball collides elastically with a 300 g ball that is at rest. If the 100 g ball was traveling in the positive x-direction at 6.20 m/s before the
collision, what are the velocities of the two
balls after the collision?

The magnitude of the velocities of the two balls after the collision is 3.1 m/s (each one).

Explanation:

We can find the velocity of the two balls after the collision by conservation of linear momentum and energy:

Where:

m₁: is the mass of the ball 1 = 100 g = 0.1 kg

m₂: is the mass of the ball 2 = 300 g = 0.3 kg

: is the initial velocity of the ball 1 = 6.20 m/s

: is the initial velocity of the ball 2 = 0 (it is at rest)

: is the final velocity of the ball 1 =?

: is the initial velocity of the ball 2 =?

(1)        

Now, by conservation of kinetic energy (since they collide elastically):

 (2)

By entering equation (1) into (2) we have:

By solving the above equation for :

Now, can be calculated with equation (1):

The minus sign of means that the ball 1 (100g) is moving in the negative x-direction after the collision.

Therefore, the magnitude of the velocities of the two balls after the collision is 3.1 m/s (each one).

I hope it helps you!                  

cant without the picture! ?

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