# 2D Momentum of automobile collision Problem

1. Jan 21, 2012

### xChee

Need help with two 2D momentum questions.

Q1: Two automobiles collide at an intersection. One car of mass 1.4x103 kg is travelling at 45km/h [south]; the other car of mass 1.3x103 ks is travelling at 39 km/h [east]. If the cars have a completely inelastic collision, what is their velocity after the collision.

- I started off by converting the units of the velocities to m/s but have no clue what to do after :/

2. Jan 21, 2012

### Poley

Because there are no external forces, the law of conservation of momentum tells us that the total momentum before the collision is equal to the total momentum after. I would calculate this momentum and then use it to find the requested velocity.

Last edited: Jan 21, 2012
3. Jan 21, 2012

### Curious3141

There is no need to convert to m/s, you can stick to km/hr if you remain consistent throughout. Just ensure that your momentum units are kg.km/h.

Start by defining 2 axes at right angles - horizontal (West-East) and vertical (North-South).

Use the principle of conservation of linear momentum independently in each axis. Final momentum = initial momentum.

Calculate the respective initial momenta in each axis. This is equal to the final momentum in the respective axis.

Calculate the respective velocity in each axis. Remember the "new mass" is the sum of the original masses since this is an inelastic collision (the cars move as one congealed mass of metal).

Now use Pythagoras theorem to calculate the overall final speed (the magnitude). Use trigonometry to find an angle (e.g. θ "South of East") to describe the direction of motion.

Write down the answer as: "The final velocity is --- km/h at an angle of --- South of East."