Hockey puck B rests on a smooth ice surface and is struck by a second puck A, which has the same mass. Puck A is initially traveling at 15.2 m/s and is deflected 30.0^\circ from its initial direction. The pucks are made of superball-like material, so you may assume that the collision is perfectly elastic.
Find the final speed of the puck A after the collision
conservation of momentum for one object at rest (1)
mvai = mvaf + mvbf
conservation of kinetic energy (2)
1/2mvai = 1/2mvaf + 1/2mvbf
The Attempt at a Solution
I have tried this about 10 times and cannot get it right :(
i solved equation 1 for the x and y components of the velocity final for puck b
vbxf = vaxi - vaxf
vbyf = -vayf
vbf = sqrt [(vaxi - vaxf)2 + (-vayf)2]
vbf = sqrt [vaxi2 - 2vaxf + vaxf2 + vayf2]
then i plugged this into 1/2mvai = 1/2mvaf + 1/2mvbf for v_bf
i would show all my steps of reducing but it would take forever.
i end up getting vfa = cos(30) = .866 but this is wrong
am i right up to this point of what i have done?
any help would be great. Thank you