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.
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\u00b0" and "\\beta\\approx26.66\u00b0" . Answer
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