Final answer:
Sam's top speed on jet-powered skis, accounting for thrust and kinetic friction, is calculated as 27.36 m/s.
Step-by-step explanation:
To determine Sam's top speed on his jet-powered skis, we consider the forces acting on him while he is in motion. The force of thrust from the skis (220 N) propels him forward, while kinetic friction opposes his movement.
Frictional force (f k) can be calculated using the coefficient of kinetic friction (μk) and the normal force (N). For Sam, who has a mass of 50 kg on level ground, the normal force is equal to the weight (N = mg), which is 50 kg × 9.8 m/s2 = 490 N. Thus, the frictional force is f k = μk × N = 0.1 × 490 N = 49 N.
Sam's acceleration (a) is determined by the net force acting on him and using Newton's second law (F = ma). Subtracting the frictional force from the thrust gives the net force: 220 N - 49 N = 171 N. The acceleration is therefore a = 171 N / 50 kg = 3.42 m/s2.
Assuming Sam starts from rest, we can use the kinematic equation v = u + at to find his top speed (v), where u is the initial speed (0 m/s), a is the acceleration (3.42 m/s2), and t is the time (8 s): v = 0 m/s + (3.42 m/s2 × 8 s) = 27.36 m/s. Therefore, Sam's top speed is 27.36 m/s.