Two cars, one with mass mi = 1200 kg is traveling north, and the other a large car with mass m2= 3000 kg is traveling East. If they collide while each car is traveling with a speed v = 5.0 m/s, what is the car's final speed and direction (vector notation can be given as well). Assume the collision is perfectly inelastic.

Both cars travel at < 10 , 4 > m/s

Explanation:

Conservation of Linear Momentum

The total momentum of a system of particles of masses m1 and m2 traveling at velocities v1 and v2 (vectors) is given by

When the particles collide, their velocities change to v1' and v2' while their masses remain unaltered. The total momentum in the final condition is

We know the collision is perfectly inelastic, which  means both cars stick together at a common final velocity v'. Thus

Both total momentums are equal:

Solving for v'

The data obtained from the question is

The first car travels north which means its velocity has only y-component

The second car travels east, only x-component of the velocity is present

Plugging in the values

The magnitude of the velocity is

And the angle