Two vehicles approach a right angle intersection and then collide. after the collision, they become entangled. if their mass ratios were 1: 4 and their respective speeds as they approached were both 13 m/s, find the magnitude and direction of the final velocity of the wreck.

To solve this problem we require the concept of conservation of momentum, applied in the particular case of collisions.

The general equation says that,

Where,

The crash occurs at an intersection so we must separate the two speeds by their respective vector: x, y.

In the case of what happened on the X axis, we have that the body M_2 has a speed = 0, this because it is not the direction in which it travels, therefore

The same analysis must be given for the particular case in the Y direction, where the mass body M_1 does not act with its velocity here, therefore:

,

We have the two components of a velocity vector given by

Get the magnitude,

With a direction given by

whichever one it is, it's definitely not one that you included on the list you provided.