What is the velocity of the surveillance plane after the collision with the smaller plane?

To determine the correct velocity of the surveillance plane after the collision with the smaller plane, it's essential to apply principles from conservation of momentum and vector addition, which are fundamental concepts in physics.

In a collision scenario involving two planes, the total momentum before the collision must equal the total momentum after the collision, assuming no external forces act on the system. This principle helps us deduce the final velocities of the involved objects.

In this case, selecting the velocity of 64.8 m/s at an angle of 13.1° north of west as the answer suggests a specific relationship between the two planes' masses and their pre-collision velocities. The angle indicates that the resulting velocity vector is neither entirely west nor entirely north but has components in both directions, showcasing a change in momentum due to the collision.

The value of 64.8 m/s signifies the combined momentum has been conservatively transferred and redistributed post-collision, resulting in this final velocity. The angle indicates an orientation that aligns with the vector results of the collision dynamics, which account for both planes' directions and speeds prior to impact.

This precise value and direction illustrate how collisions can result in modifications to both speed and trajectory, highlighting essential concepts related to the conservation of momentum and the vector