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midterm exam 2 solutions

# Physics for Scientists and Engineers (3rd Edition)

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PHY131 Midterm-II Exam April 9, 2003 Solutions 1) (20 points) An arrow (mass m = 200 g) travels east with a speed of 150 m/s. It hits a duck (mass M = 2.0 kg) flying north at 25 m/s. The arrow gets stuck in the dead duck. a) At what angle (north of east) does the dead duck (plus the stuck arrow) travel immediately after the hit? Inelastic collision => linear momentum is conserved: after before p p r r = Version A: Momentum component in east direction: s / kgm 30 s / m 150 kg 2 . 0 mv p east = × = = Momentum component in north direction: p s / kgm 50 s / m 25 kg 0 . 2 MV north = × = = Direction (north of east): 0 east north 59 ) 3 / 5 tan( a ) p / p tan( a = = = θ Version B: Momentum component in north direction: p s / kgm 30 s / m 150 kg 2 . 0 mv north = × = = Momentum component in east direction: s / kgm 50 s / m 25 kg 0 . 2 MV p east = × = = Direction (north of east): 0 east north 31 ) 5 / 3 tan( a ) p / p tan( a = = = θ b) What is the speed of duck and arrow just after the hit? s / m 5 . 26 ) M m /( p p ' v ' v ) M m ( p p | p | 2 north 2 east 2 north 2 east after = + + = + = + = r c) What is the difference between the kinetic energies before and after the hit?

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