Final answer:
The student's physics problem involves solving for the final velocity of two cars that collide and stick together, using the principle of momentum conservation in two dimensions and the Pythagorean theorem to find the magnitude and direction.
Step-by-step explanation:
The question involves a two-dimensional collision in the field of Physics, specifically concerning the conservation of momentum. To solve the problem, we apply the principle of conservation of momentum separately in the south and west directions as the collision is perfectly inelastic, meaning the two cars stick together after the collision.
To find the final velocity of the combined mass of the cars, we must consider the conservation of momentum in both the south and the west directions.
The initial momentum in the south direction is from the first car (mass 1100 kg × velocity 6.5 m/s), and the initial momentum in the west direction is from the second car (mass 950 kg × velocity 19.5 m/s). After the collision, the combined mass of the two cars will have a southward momentum and a westward momentum.
By applying the Pythagorean theorem to these momentum components, we can find the magnitude of the final velocity.
To determine the direction, we use the arctangent function (inverse tangent) to find the angle of the resulting velocity vector relative to the westward direction.