Question

A mass M travels at a speed V in the forward x- direction: It explodes into two pieces: one with mass m1 the other with mass m2. The mass m1 moves at an angle φ1 above the x-axis and the mass m2 moves at an angle φ2 below the x-axis. Both angles are directed in the forward direction. Find the magnitues of the momenta of the two pieces in terms of M V and the two angles

Answer 1

M = m1 + m2

P = p1 + p2

p1x = m1v1 cos(phi1)

p2x = m2v2 cos(phi2)

p1y = m1v1 sin(phi1)

p2y = m2v2 sin(phi2)

Conservation of momentum in Y direction

0 = m1v1 sin(phi1) + m2v2 sin(phi2)

m1v1 sin(phi1) = -m2v2 sin(phi2)

P1 sin(phi1) = -P2 sin(phi2)

P1 = -P2 sin(phi2)/sin(phi1)

in X direction

MV = m1v1 cos(phi1) + m2v2 cos(phi2)

MV = P1 cos(phi1) + P2 cos(phi2)

MV = -P2 sin(phi2)/sin(phi1) + P2 cos(phi2)

P2 = MV/(cos(phi2) - sin(phi2)/sin(phi1))

P1 = -MV/(cos(phi2) - sin(phi2)/sin(phi1)) [sin(phi2)/sin(phi1)]