Well, it seems like A and B had a little rendezvous and decided to stick together. Let's see what happens.
To find the final velocity of the two-object system, we need to use the law of conservation of momentum. The total initial momentum of the system is equal to the total final momentum of the system.
Now, the momentum of an object is mass times velocity. So, the initial momentum of object A is 17.0 kg * 8.15 m/s (due east), while the initial momentum of object B is 28.0 kg * 4.85 m/s (due north).
To add up the momenta, we have to consider the directions. Since object A is moving east and object B is moving north, we need to use vector addition to determine the direction of the total momentum.
To do this, we can find the components of the initial velocities of A and B using trigonometry. The component of A's initial velocity in the north direction is A_north = 8.15 m/s * sin(90°), while the component of B's initial velocity in the east direction is B_east = 4.85 m/s * cos(90°).
Adding up these components, we get the total initial momentum in the east direction (Px_initial) and the total initial momentum in the north direction (Py_initial).
Now, because momentum is conserved, the total initial momentum in the east direction should be equal to the total final momentum in the east direction (Px_final), and the total initial momentum in the north direction should be equal to the total final momentum in the north direction (Py_final).
Finally, we can find the magnitude of the final velocity of the two-object system by using the Pythagorean theorem.
Now, let me grab my calculator and do the math for you.