A car with a mass of 2500 kg and moving at 3 m/s northeast collides with a 3000 kg car moving northwest at 2.5 m/s . Find their final velocities. Assume a perfectly inelastic collision.
Let's choose the axes as shown in the figure below.
In a perfectly inelastic collision the momentum conservation law still holds. Thus, the total momentum before the collision in the projection on the x-axis is:
is equal to the total momentum after the collision in the projection on the x-axis:
where are the masses of the cars, are their speeds before the collision, and is their speed after the collsion in x-direction. Thus, obtain:
Similarly, the momentum conservation law in the projection on y-axis gives:
where is car's speed after the collsion in y-direction. Thus, obtain:
Thus, the final velocity is:
Answer. .
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