The stoplight had just changed and a 1900 kg cadillac had entered the intersection, heading north at 2.0 m/s , when it was struck by a 1200 kg eastbound volkswagen. the cars stuck together and slid to a halt, leaving skid marks angled 35∘ north of east. part a how fast was the volkswagen going just before the impact?

The velocity of the Volkswagen is approximately 2.59 m/s

Explanation:

I have attached an image containing what I try to explain below (note: I am not a graphic designer. It's MS Paint. I apologize for its simplicity.)

Let's start by evaluating the conceptual stuff. The two vehicles collided and stuck together, meaning that this was an inelastic collision; an elastic collision question would have specified that energy was conserved (and, more than likely, specified that it was an elastic collision). In an inelastic collision, momentum is conserved but energy is not - the only equation we can use to calculate the basic stuff is the momentum equation.

Momentum is calculated as P=mv, where m is the mass of the object and v is its relative velocity. In this case, the momentum of the Cadillac is measured to be 1900 kg times 2 meters per second, or 3800 Newtons moving northbound.

Because a final position is not specified, we're going to have to get even more conceptual. The Cadillac was moving northbound, while the Volkswagen was moving eastbound, and the collision made them move in a complex direction. If the Cadillac and Volkswagen had the exact same momentum, they would have collided and proceeded to move in the net direction of 45 degrees northeast. However, because the skid marks show that the cars moved 35 degrees northeast, one of the cars had more momentum. The tracks are moving more northward than they are eastward, meaning that the Cadillac had more momentum than the Volkswagen.

We can use a little trigonometry to tie all of this together. We know that the Cadillac with a northbound momentum of 3800 Newtons contributed all of the "north" in the complex direction after the accident, while the Volkswagen contributed all of the "east" in the complex direction after the accident. Since the crash is at 35 degrees, we should expect the momentum of the Volkswagen to be less than that of the Cadillac. To calculate, we can take the cosine of the angle to relate all of this together.

cos 35 = opposite/adjacent (y-axis is north/south, x-axis is east/west, remember that the angle is between the y-axis and the complex momentum)

cos 35 = x N/ 3800 N

x = 3112.8 N

The Volkswagen had a momentum of 3112.8 N; however, the problem is asking for the velocity of the car. Simply plug this along with the mass of the car into P=mv and solve for the velocity: 2.59 meters per second.