One object weighing 26 kg is moving parallel to the x-axis at 12 m/s. The other object weighing 10 kg is moving parallel to the y-axis at 16 m/s. The two objects undergo an inelastic collision and stick to each other. The total momentum of the objects is conserved whether the collision is elastic or inelastic. After collision, the resulting object weighs 36 kg. The component of the velocity of the resulting object parallel to the x-axis is (26*12)/36 = 26/3 m/s and the component of the velocity of the resulting object parallel to the y-axis is (10*16)/36 = 40/9 m/s.
The magnitude of the resultant velocity is the square root of the square of the perpendicular components.This is equal to 9.73 m/s.
The direction of the velocity is an angle made with the positive x-axis equal to arc tan of the y component divided by the x component. This gives an angle of 27.14 degrees to the positive x-direction.