Question

a 5kg ball with a velocity of 10m/a in the positive horizontal direction collides with a 4 kg ball at rest; the collision is elastic and the velocity of the 5kg ball after the collision is 8m/s, what is the final speed of the 4 kg ball? If the 4kg ball is deflected 37 degrees below the horizontal, what angle is the 5kg ball deflected to?

Answer 1

Since the collision is elastic,

1) The Kinetic energy of the system before and after collision is the same

2) The momentum of the system before and after collision is same

To calculate the final velocity of the 4 kg ball, we equate the kinetic energies before and after collision:

Since m₂ is initially at rest, v₂=0. Plugging in the known values, we have

Now, we need to calculate the angle :

So we use the law of conservation of linear momentum:

    (Since v2 = 0)

We consider the X and Y components of separately:

         Since initial velocity of the 5kg ball is along X-axis, its Y-component is zero.  

         Y-component of

         Y-component of (negative because it's in the negative Y-direction)

Thus, we have from the above equation:

So the 5 kg ball is deflected by