Question

Two cars approach an ice-covered intersection. One car, of mass 1.21 X 10^3 kg, is initially traveling north at 12.1 m/s. The other car, of mass 1.62 X 10^3 kg, is initially traveling east at 12.1 m/s. The cars reach the intersection at the same instant, collide, and move off coupled together. Find the velocity of the center of mass of the two-car system just after the collision.

magnitude: ______

direction: _____ north of east

Answer 1

here,

the mass of car 1 , m1 = 1210 kg

the mass of car 2 , m2 = 1620 kg

the initial velocity of car 1 , u1 = 12.1 j m/s

the initial velocity of car 2 , u2 = 12.1 i m/s

let the final velocity of the combination be v

using conservation of momentum

m1 * u1 + m2 * u2 = (m1 + m2) * v

1210 * 12.1 j + 1620 * 12.1 i = ( 1210 + 1620) * v

v = 6.93 i m/s + 5.17 j m/s

the magnitude of the velocity of the center of mass of the two-car system just after the collision , |v| = sqrt(6.93^2 + 5.17^2) = 8.64 m/s

the direction of velocity , theta = arctan(5.17 /6.93) = 36.7 degree North of East