A 50.0-kg skater is traveling due east at a speed of 3.00 m /s. A 70.0-kg skater is moving due south at a speed of 7.00 m/s. They collide and hold on to each other after the collision, managing to move off at an angle θ south of east, with a speed of vf. Find

(a) The angle θ and

(b) The speed vf, assuming that friction can be ignored.