A0.500-kilogram cart traveling to the right on a horizontal, frictionless surface at 2.20 meters per second collides head on with a 0.800-kilogram cart moving to the left at 1.10 meters per second. what is the magnitude ofthe total momentum of the two-cart system after the collision?

Consider the motion towards right as positive and motion towards left as negative.

m₁ = mass of the cart moving to right = 0.500 kg

v₁ = initial velocity before collision of the cart moving towards right = 2.2 m/s

m₂ = mass of cart moving to left = 0.800 kg

v₂ = initial velocity before collision of the cart moving towards left = - 1.1 m/s

initial momentum of the system of carts before the collision is given as

P₁ = m₁ v₁ + m₂ v₂

P₁ = (0.500) (2.2) + (0.800) (- 1.1)

P₁ = 0.22 kgm/s

P₂ = momentum of system of carts after collision

As per conservation of momentum,

Momentum of system of carts after collision = Momentum of system of carts before collision

P₂ = P₁

P₂ = 0.22 kgm/s

at positions a, g kinetic energy is maximum.

at position d, potential energy is maximum.