Question

One train car of mass 50,000 kg (50 Mg) is moving 6.0 m/s to the south on a frictionless track and couples with another car of mass 20,000 kg (20 Mg). The final velocity of the now-coupled cars is 1.8 m/s to the south. Find the velocity of the second car before the coupling. (Hint: The direction is important!)

Answer 1

here,

mass of car 1 , m1 = 50000 kg

initial speed of car 1 , u1 = 6 m/s j

mass of car 2 , m2 = 20000 kg

the final velocity after coupling , v = 1.8 m/s j

let the initial speed of second car be u2

using conservation of momentum

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

50000 * 6 j + 20000 * u2 = ( 50000 + 20000) * 1.8 j

solving for v

v = - 8.7 m/s j

the speed of second car is 8.7 m/s to the North