Inelastic Collision Scenario Question

[IronManTable]

Homework Statement

A railway carriage with a mass m = 2.45×10⁴ kg is initially traveling to the left with a speed Vi = 3.33 m/s. It collides and couples with (get stuck to) two identical railway carriages move to the left with a speed of Ui = 1.69 m/s.

1. What is the speed of the railway carriage after the collision? (give a negative answer if the speed is to the right.)

2. How much kinetic energy is lost in this collision?

Homework Equations

P = m₁v₁ + m₂v₂

KE = 1/2mv²

KE (before collision) = 1/2m₁v₁² + 1/2m₂v₂²

KE (after collision) = 1/2(m₁+ m₂)v_f²

The Attempt at a Solution

1. P = (2.45×10⁴ x 3.33) + 2(2.45×10⁴ x 1.69)
= 1.6x10⁵ kgms^-1

∴ P = 1.6x10⁵ = (m₁ + 2m₂)vf = 7.35x10⁴vf
vf = (1.6x10⁵) / (7.35x10⁴)
vf = 2.18 m/s

2.
KE (before collision) = 1/2m₁v₁² + 1/2m₂v₂²
KE (before collision) = 1/2(2.45×10⁴ x (3.33)²) + 1/2(2(2.45×10⁴ x (1.69)²)
= 2.06x10⁵ J

KE (after collision) = 1/2(m₁+ m₂)v_f²
KE (after collision) = 1/2( 2.45×10⁴+ 2(2.45×10⁴) ) x (2.18)²
= 1.75x10⁵ J

KE lost = 3.1x10⁴ J

Thank you for any help :)

 

[HallsofIvy]

That's what I get.

 

[IronManTable]

So I assume my working out and answers are correct?