A 26.5-g object moving to the right at 20.5 cm/s overtakes and collides elastically with a 12.5-g object moving in the same direction at 15.0 cm/s. Find the velocity of each object after the collision. (Take the positive direction to be to the right. Indicate the direction with the sign of your answer.)

v₁ =0.19 m/s and v₂ = 0.18 m/s

Explanation:

By conservation of energy and conservation of momentum we can find the velocity of each object after the collision:

Momentum:

Before (b) = After (a)

    (1)      

Energy:

Before (b) = After (a)                        

  (2)    

From equation (1) we have:

  (3)

Now, by entering equation (3) into (2) we have:  

   (4)

By solving equation (4) for , we will have two values for

We will take the average of both values:

Now, by introducing this value into equation (3) we can find :

Therefore, the velocity of object 1 and object 2 after the collision is 0.19 m/s and 0.18 m/s, respectively.

I hope it helps you!    

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