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# notes9a - Example A 45-kg swimmer runs with a horizontal...

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Example A 45-kg swimmer runs with a horizontal velocity of +5.1 m/s off of a boat dock into a stationary 12-kg rubber raft. Find the velocity that the swimmer and raft would have after impact, if there were no friction and resistance due to the water. Solution: Given: m 1 = 45 kg, m 2 = 12 kg, Find: v i 1 = + 5.1 m s ˆ x , v i 2 = 0 ? v , v 2 1 = f f

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Consider motion of boy and raft just before and just after impact Boy and raft define the system Neglect friction and air resistance no external forces (which act in the direction of motion) Therefore, we can use the Conservation of Linear Momentum 2 2 1 1 2 2 1 1 2 1 2 1 f f i i f f i i f i m m m m p p p p P P v v v v + = + + = + = 1 v i
f f f v v v 2 1 = = Since, the boy moves with the raft after the impact m 1 v i 1 = ( m 1 + m 2 )v f v f = m 1 ( m 1 + m 2 ) v i 1 = 45 (45 + 12) 5.1 = 4.0 m s v f = + 4.0 m s ˆ x = v f 1 = v f 2 What if we have the case where v f1 v f2 ? We then have two unknowns. So, we need another equation.

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m 1 v i 1 = m 1 v f 1 + m 2 v f 2 Return to the boy and the raft conservation of momentum problem. But let’s assume that the boy misses the raft. Then, the final velocities of the boy and raft
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notes9a - Example A 45-kg swimmer runs with a horizontal...

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