Question

Two cars collide at an icy intersection and stick together afterward. The first car has a mass of 1450 kg and is approaching at 8.5 m/s due south. The second car has a mass of 850 kg and is approaching at 16.5 m/s due west.

(a) Calculate the magnitude of the final velocity, in meters per second, of the cars.

(b) Calculate the direction of the final velocity, in degrees south of west, of the cars.

(c) What is the change in kinetic energy, in joules, for the collision? (This energy goes into deformation of the cars.)

Answer 1

PART A:

Taking east as positive x-direction and north as positive y-direction. The initial momentum of the system is

Now, when they collide, they get stuck and the mass of the two vehicles adds up. The final momentum thus can be given by

The conservation of momentum gives us

So, the magnitude of the final velocity is 8.12 m/s.

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PART B:

The velocity vector points in 3rd quadrant. And the angle from negative x axis is

So, the direction of the velocity is 41.3o South of West.

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PART C:

The initial energy of the system is

And the final energy of the system is

So, the change in the kinetic energy is

So, the answer to this part is 92262.94 J.