A 15K N automobile travels at a speed of 45 km/h northwardsalong a street, and a

Question

A 15K N automobile travels at a speed of 45 km/h northwardsalong a street, and a 7500 N sports car travels at a speed of40km/h eastward along an intersecting street. (a) if nietherdrivers brake and the cars collide at the intersection and sticktogether, what will the speed and the direction of the carsimmediately after the collision ? (b) What percentage ofthe initial kinetic energy will be lost in thecollision? My answer to (a) is 130 m/s at 56.30 northeast. I can't think of the percentage ofenergy is lost. A 15K N automobile travels at a speed of 45 km/h northwardsalong a street, and a 7500 N sports car travels at a speed of40km/h eastward along an intersecting street. (a) if nietherdrivers brake and the cars collide at the intersection and sticktogether, what will the speed and the direction of the carsimmediately after the collision ? (b) What percentage ofthe initial kinetic energy will be lost in thecollision? My answer to (a) is 130 m/s at 56.30 northeast. I can't think of the percentage ofenergy is lost.

Explanation / Answer

final velocity = v vx = (7500*40)/(7500 + 15000) = 40/3 km/h vy = (15000*45)/(7500 + 15000) = 90/3 km/h speed v = (402 + 902) /3 = 32.8 km/h =32.8/3.6 m/s = 9.12 m/s = arctan(9/4) = 66.0o north of east kinetic energy lost = (7500/9.8)*(40/3.6)2/2 +(15000/9.8)*(45/3.6)2/2 - [(7500 +15000)/9.8]*9.122/2 = 7.15*104 J

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