Question

An elastic collision of two pucks (mA = 0.5 kg, mg = 0.3 kg) on a frictionless air-jockey table. Puck A has an initial velocity of 4m/s in the positive X-direction and a final velocity of 2m/s in an unknown direction a. Puck B is initially at rest. Find the final speed of puck B and the angles a and b.

Answer 1

For an elastic collision

X: $Mv=mu'\cdot \cos\beta+Mv'\cdot\cos\alpha$

Y: $mu'\cdot \sin\beta=Mv'\cdot\sin\alpha$

KE: $Mv^2/2=mu'^2/2+Mv'^2/2 \to$

$0.5\cdot4^2/2=0.3\cdot u'^2/2+0.5\cdot 2^2/2\to u'=4.47(m/s)$ .Answer

$0.5\cdot 4=0.3\cdot 4.47\cdot \cos\beta+0.5\cdot 2\cdot\cos\alpha$

$0.3\cdot 4.47\cdot \sin\beta=0.5\cdot 2\cdot\sin\alpha\to$ $\alpha\approx36.99°$ and $\beta\approx26.66°$ . Answer