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# Answer to Question #5423 in Electric Circuits for jessica

Question #5423
On July 25, 1956, the linear Andrea Doria, of mass 4.1x10^7 kg, was heading west at 40 km/hr. it collided off Nantucket Island with the Stockholm, of mass 1.7x10^7 kg, sailing 30 km/hr in the direction 20 degrees east of north. the bow of the Stockholm temporarily lodged in the side of the Andrea Doria; that is, the collision was perfectly inelastic.
a) find their common velocity (speed and direction) just after collision

b) what was the loss in kinematic energy due to the collision?
1
2011-12-06T08:47:46-0500
<img style="width: 155px; height: 48px;" src="data:image/png;base64,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" alt="">
Let`s use the law of conservation of momentum
<img style="width: 101px; height: 41px;" src="data:image/png;base64,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" alt="">
We write this equation in terms of projections on the axis x (West) and y (North)
We find the difference of the kinetic energy of all the bodies before the collision and its aftermath.
<img style="width: 447px; height: 29px;" src="data:image/png;base64,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" alt="">

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