Momentum help plz!!!?

Question

A father (m=80 kg) and his son (m-40 kg) are ice skating toward each other at an angle of 30 degrees, son is moving towards the x axis at an angle of 30 degrees to the father and father is moving straight toward the origin. Both father and son have a speed of 2.5 m/s. Where they meet the son jumps on top of the father and they slide together acroos the ice.
Determine the magnitude and direction of their common speed just after the collision.

Answer 1

Momentum is conserved in each dimension.

Let the motion of the father define the +x direction. Then the initial momentum on the x-axis is

( 80 kg ) ( 2.5 m / s ) - ( 40 kg ) ( 2.5 m / s ) ( cos 30 )

and on the y-axis is

( 40 kg ) ( 2.5 m / s ) ( sin 30 )

Now they collide. The final momentum on the x-axis is

( 80 kg + 40 kg ) vx

and the final momentum on the y-axis is

( 80 kg + 40 kg ) vy

Set the initial and final x- momenta equal and solve for vx.
Set the initial and final y- momenta equal and solve for vy.
v = sqrt ( vx² + vy² )
The angle relative to the positive x-axis is int-tan ( vy / vx )