Fezzik and the Dread Pirate Roberts run into each other head on (elastic collisi

Question

Fezzik and the Dread Pirate Roberts run into each other head on (elastic collision) while traveling with the same initial speed. Fezzik has twice the mass of the Dread Pirate Roberts.
A. Show that momentum is conserved if the two men form an isolated system.
B. Using Newton’s third law show that the impulse delivered to Fezzik by Roberts is the same magnitude as the impulse delivered to Roberts by Fezzik.
C. Find the final velocity of each man.
D. Find the final velocity, if Roberts manages to grasp and hang on the Fezzik.

Explanation / Answer

m1 = m   (Robert) m2 = 2m (Fezzik) v1i = u v2i = - u (A) Momentum before collision P1 = m1v1i + m2v2i = mu + 2m(-u)                                                                         = - mu   ------------(1) Final velocites : v1f = -0.333*u + 1.333(-u) = -1.666u v2f = 0.666u + 0.333(-u) = 0.333u Momentum after collision P2 = m1v1f + m2v2f = -1.666mu + 2m(0.333u)                                                                       = - mu    --------------(2) From (1) & (2) , momentum is conserved if the two men form an isolated system. (B) From newtons third law                           F12 = F21                        F12 t = F21 t     where t = time of contact   So, the impulse delivered to Fezzik by Roberts is the same magnitude as the impulse delivered to Roberts by Fezzik. (C)
v1f = -0.333*u + 1.333(-u) = -1.666u v2f = 0.666u + 0.333(-u) = 0.333u Momentum after collision P2 = m1v1f + m2v2f = -1.666mu + 2m(0.333u)                                                                       = - mu    --------------(2) From (1) & (2) , momentum is conserved if the two men form an isolated system. (B) From newtons third law                           F12 = F21                        F12 t = F21 t     where t = time of contact   So, the impulse delivered to Fezzik by Roberts is the same magnitude as the impulse delivered to Roberts by Fezzik. (C)
v1f = -0.333*u + 1.333(-u) = -1.666u v2f = 0.666u + 0.333(-u) = 0.333u (D) Let v be the final common velocity From law of conservation of momentum                        m1v1i + m2v2i = (m1 + m2)v                                     - mu   = 3m v                                            v = - (u/3) In the direction of Fezzik                

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