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 3.5 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 7.5 kg and is initially at rest. After the collision, the two pucks fly apart with the angles shown in the drawing. PLEASE HELP!

The drawing shows a collision between two pucks on an air-hockey table. Puck A has a mass of 3.5 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 7.5 kg and is initially at rest. After the collision, the two pucks fly apart with the angles shown in the drawing.

Explanation / Answer

Use conservation of momentum
let U = initial speed and V = final speed
the initial momentum (pi) = MaUa + 0 = 3.5(5.5) = 19.25 kg*m/s (right)
not that pi in the x direction is 19.25 and pi in the y-direction is 0. By conservation of momentum, pf(x) = pi(x) and pf(y) = pi(y)

MaVa(x) + MbVb(x) = 19.25

MaVa(y) - MbVb(y) = 0
3.5Va(cos65) + 7.5Vb(cos37) = 19.25 and 3.5Va(sin65) - 7.5Vb(sin37) = 0

from the equation on the right, 7.5Vb = 3.5Va(sin65)/(sin37) ****
substituting into the equation on the left:

3.5Va(cos65) + 3.5Va(sin65)/(sin37) = 19.25

Va = 19.25 / (3.5cos65 + 3.5sin65/sin37)

Va = 2.85 m/s

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