Final answer:
The combined kinetic energy of Derek and his bike is 1549.57 J.
Step-by-step explanation:
The combined kinetic energy of Derek and his bike can be calculated using the principle of conservation of momentum. According to the problem statement, the final velocity of the combined mass is 4.286 m/s. We can calculate the initial kinetic energy using the formula KE = 0.5 * mass * velocity^2. Therefore, the initial kinetic energy is (0.5)(60)(4.286)^2 = 1549.57 J.