The drawing shows a collision between two pucks on an air-hockey table. Puck A h

Question

The drawing shows a collision between two pucks on an air-hockey table. Puck A has a mass of 0.036 kg and is moving along the x axis with a velocity of +5.5 m/s. It makes a collision with puck B, which has a mass of 0.056 kg and is initially at rest. The collision is not head-on. After the collision, the two pucks fly apart with the angles shown in the drawing.

The drawing shows a collision between two pucks on an air-hockey table. Puck A has a mass of 0.036 kg and is moving along the x axis with a velocity of +5.5 m/s. It makes a collision with puck B, which has a mass of 0.056 kg and is initially at rest. The collision is not head-on. After the collision, the two pucks fly apart with the angles shown in the drawing. Find the final speed of puck A. m/s Find the final speed of puck B. m/s

Explanation / Answer

Let's call the 2 velocities Va and Vb, the 2 masses Ma and Mb, and the 2 angles Pa and -Pb.
Since there was no momentum earlier in the y-direction, the resulting momenta of the 2 pucks in the y-direction must cancel each other:
Ma Va sin Pa - Mb Vb sin Pb = 0

Also, resulting net momentum in the x-direction must equal the initial:
Ma Va cos Pa + Mb Vb cos Pb = Ma V, where V is the initial velocity of A.

Substituting known numerical values:
0.036 Va sin 65 - 0.066 Vb sin 37 = 0
0.036 Va cos 65 + 0.066 Vb cos 37 = 0.036 x 5.5

Solve the simultaneous equation to obtain Va and Vb.
Hint: multiply the 1st by cos 37 and the 2nd by sin 37 and add to get Va.





Va = 3.38 m/s, Vb = 2.78 m/s

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