You and your friends are doing physics experiments on a frozen pond that serves as a frictionless horizontal surface. sam, with a mass of 80.0 kg, is given a push and slides eastward. abigail, with a mass of 50.0 kg, is sent sliding northward. they collide and, after the collision, sam is moving at 6.00 m/s in a direction 37.0° north of east, while abigail is moving at 9.00 m/s in a direction 23.0° south of east. find the speeds of sam and abigail just before the collision.

Velocity of Sam = and velocity of Abigail = Explanation: Consider Vs as sam velocity and Va  as bigail velocity.  Now consider the north as positive x  and the east as positive y for our reference.  Before collision, their velocity vectors can be represented as                           = Vs i    =Va j  Now after collision their velocity vectors are given as = 6 cos 37 i + 6 sin 37 j   = 4.79 i + 3.61 j = 9 cos 23 i + 9 sin 23 j  = 8.28 i - 3.52 j  As we know in the absence of external force the momentum before and after collision will remain the same therefore                  P1 = P2    ∴ P = mv Momentum = mass x velocity                As sliding is on frictionless surface therefore before and after the collision, momentum remains conserved in the absence of external force. we can write it as                        Now putting values we get         80 x Vs + 50 x 0  =  80 x 4.79 + 50 x 8.28  (First Consider horizontal vector components)                         Velocity of sam before collision= Vs = 9.97 Now consider vertical vector components              80 x 0 +  50 x Va = 80 x 3.61 + 50 x (-3.52) (Before Collision direction opposite so put negative sign)                  velocity of abigail before collision = Va = 2.26  

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