Final answer:
To find how fast the enmeshed cars were moving just after the collision, conservation of momentum is used. The velocities are broken into components, which are then used to calculate the final velocity magnitude and direction using trigonometric relationships.
Step-by-step explanation:
The question is concerned with a two-dimensional inelastic collision between two cars at an intersection. When two objects collide and move together after the collision, the situation is best analyzed using conservation of momentum.
To determine how fast the enmeshed cars were moving just after the collision, we can use the principle of conservation of linear momentum, which states that the total momentum of a closed system remains constant if no external forces act upon it. The vector sum of the momenta of Car A and Car B before collision will equal the momentum of the enmeshed cars just after the collision. We can calculate this by breaking down the velocities into x and y components and applying the conservation of momentum in each direction.
The final step is to find the magnitude and direction of the velocity of the enmeshed cars using the resultant components of momentum in each direction. If the cars are moving at an angle of 60 degrees south of east, it can be deduced that the x-component of the final velocity is to the east, and the y-component is to the south. The magnitude of the final velocity (v) of the enmeshed cars can be found using the equation v = \sqrt{(v_x)^2 + (v_y)^2}, where v_x and v_y are the x and y components of the final velocity, respectively. The direction (\theta) with respect to east can be determined by \theta = \arctan(v_y / v_x).