A 15500 N automobile travels at a speed of 49 km/h northward along a street, and

Question

A 15500 N automobile travels at a speed of 49 km/h northward along a street, and a 6500 N sports car travels at a speed of 58 km/h eastward along an intersecting street.
(a) If neither driver brakes and the cars collide at the intersection and lock bumpers, what will the velocity of the cars be immediately after the collision?
magnitude _________ km/h
direction ________ ° (counterclockwise from due east)

(b) What percentage of the initial kinetic energy will be lost in the collision?
___________ %

Explanation / Answer

let north be +ve Y and east be +ve X

a) by conservation of momentum the speed will be 15500*49/(15500+6500) j + 6500*58/(15500+6500) i

so the velocity will be = 34.5227j + 17.13636 i

so the speed is (34.52272 + 17.1362) = 38.541 kmph

and direction is =tan-1(34.5227/17.136) = 63.6 degrees counterclockwise from due east

b) KE initial = 29540750

KE final = 16339495

so % lost = 44.68%

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