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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.

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usamakld99
  1. Answer: Velocity of Sam = [tex]9.97ms^{-1}[/tex] and velocity of Abigail = [tex]2.26 ms^{-1}[/tex] 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                           [tex]Vs_{1}[/tex] = Vs i   [tex]Va_{1}[/tex]  =Va j  Now after collision their velocity vectors are given as [tex]Vs_{2}[/tex] = 6 cos 37 i + 6 sin 37 j   = 4.79 i + 3.61 j [tex]Va_{2}[/tex] = 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               [tex]m_{1} v_{1} =m_{2}v_{2}[/tex]  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                      [tex]m_{s} v_{s1} + m_{a}v_{a1}  = m_{s}v_{s2}  +m_{a} v_{a2}[/tex]  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[tex]ms^{-1}[/tex] 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[tex]ms^{-1}[/tex]