car x collides with car y. how does the momentum of each car change after the collision (assume similar mass)?

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09-12-2022
Physics

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car x collides with car y. how does the momentum of each car change after the collision (assume similar mass)?

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qwmaroon qwmaroon · Answer 1 · 2022-12-15T12:44:11-05:00

We use the law of conservation of momentum (p1 = p2 in both the x- and y-direction.

Let Car A, with a mass of 2000 kg, is going from west to east, while car B, with a mass of 1500 kg, is going from north to south at 15 m/s.

First, I try to find the momentum in the x-direction with the equation p1x = p2x. I insert the values from the problem statement:

x-dir. 2000 kg * Va1x + 1500 kg * 0 m/s = (2000 kg + 1500 kg) * Vabx * cos 65° y-dir. = 2000 kg * 0 m/s + 1500 kg * 15 m/s = 3500 kg * very * sin 65° very = (1500 kg * 15 m/s) / (3500 kg * sin 65°) = 7.1 m/s with the value for very, I try to find the value for the second side and the hypotenuse with trigonometry:

Vabx = Vaby / sin ∅ = 7.1 m/s / sin 65° = 7.83 m/s. With the Pythagorean theorem, I can now find the hypotenuse and the velocity that the two enmeshed cars have: Vab = √(7.12 + 7.832) = 10.6 m/s.

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