Two cars collide at an icy intersection and stick together afterward. The first

Question

Two cars collide at an icy intersection and stick together afterward. The first car has a mass of 1750 kg and was approaching at 8.00 m/s due south. The second car has a mass of 750 kg and was approaching at 16.0 m/s due west.

Explanation / Answer

a). let the final velocity of the cars be v. from conservation of momentum in vertical direction; initial momentum of 1st car in vertical direction +initial momentum of 2nd car in vertical direction = final momentum of both cars in vertical direction => 1750*8 + 750*0 = (1750+750)*Vy => Vy = 5.6 m/s (towards south) from conservation of momentum in horizontal direction; initial momentum of 1st car in horizontal direction +initial momentum of 2nd car in horizontal direction = final momentum of both cars in horizontal direction => 1750*0 + 750*16 = (1750+750)*Vx => Vx = 4.8 m/s (towards west) total final velocity = sqrt(4.8^2 + 5.6^2) = 7.376 m/s b). direction = tan^-1(5.6/4.8) = 49.399 degrees counterclockwise from west = +49.399 degrees c). K.E. lost = initial K.E. - final K.E. => K.E. lost = [(0.5*1750*8^2) +(0.5*750*16^2)] - [0.5*(1750+750)*7.376^2] = 83993.28 J

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