Question

A red car of mass m is heading north (direction 0°). It collides at an intersection with a yellow car of mass 1.3m heading east (direction 90°). Immediately after the collision, the cars lock together and travel at in direction 42°. What is the speed of the yellow car just before the collision?

Answer 1

To find the speed of the yellow car just before the collision, we can break its initial velocity into its x-component and y-component. After the collision, since the cars travel together in a combined wreckage, the velocity of the wreckage will have both x and y components.

Step-by-step explanation:

To find the speed of the yellow car just before the collision, we can break its initial velocity into its x-component and y-component. The x-component of the yellow car's velocity can be found by multiplying its speed by the cosine of the angle, while the y-component can be found by multiplying the speed by the sine of the angle. Since the red car is heading north, its y-velocity component is 0. After the collision, since the cars travel together in a combined wreckage, the velocity of the wreckage will have both x and y components. Using trigonometry, we can find the speed of the yellow car just before the collision.

Answer 2

After the collision, the momentum to the north comes completely from the red car, and the momentum to the east comes completely from the yellow car. Suppose the initial velocity of red car is v1, and yellow car is v2. The momentum of red car is v1*m, and yellow car is v2*1.3m. Since the cas travel in direction 42, we know that tan42=1.3m*v2/m*v1, so v2/v1=0.69. The yellow car's initial velocity is 0.69 of that of the red car.