A 200 Ib student sits on a 25 Ib chair. The radius of gyration of the student is 0.3 ft, and the chair's radius of gyration is 0.2ft. The student and chair are rotating at 10 rad/s. A 30 Ib backpack is thrown at the student, who reaches out 1.5 ft from their center line to grap the backpack. Now the system rotates at 15 rad/s. What was the initial linear speed of the backpack?