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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?
Expert's answer
<img style="width: 296px; height: 203px;" 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" alt="">
<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)
<img src="data:image/png;base64,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" alt="">
<img src="data:image/png;base64,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" alt="">
We find the difference of the kinetic energy of all the bodies before the collision and its aftermath.
<img src="data:image/png;base64,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" alt="">
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