Answer
The final speed is $~~3.06~m/s$
Work Step by Step
If the collision is completely inelastic, then the y-component of the momentum cancels out and only the x-component of the momentum remains after the collision.
We can use conservation of momentum to find the final speed after the collision:
$p_{xf} = p_{xi}$
$(2m)~v_f = m~(4.00~m/s)~cos~40.0^{\circ}+m~(4.00~m/s)~cos~40.0^{\circ}$
$(2m)~v_f = 2m~(4.00~m/s)~cos~40.0^{\circ}$
$v_f = (4.00~m/s)~cos~40.0^{\circ}$
$v_f = 3.06~m/s$
The final speed is $~~3.06~m/s$.
