Jason takes off across level water on his jet-powered skis.The combined mass of Jason and his skis is 75 kg (the mass of the fuel is negligible).The skis produce a forward thrust of 200 N and have a coefficient of kinetic friction with water of 0.10.Unfortunately,the skis run out of fuel after only 41 s.How far from his starting point has Jason traveled when he finally coasts to a stop?
A)3,900 m
B)2,900 m
C)2,000 m
D)1,400 m

Question

Quizplus · Accepted Answer

The net force while the skis are powered is 200 N - (0.10 * 75 kg * 9.8 m/s²) = 127.5 N. The acceleration is 127.5 N / 75 kg = 1.7 m/s². Using the formula d = v₀t + 0.5at², with v₀ = 0, t = 41 s, and a = 1.7 m/s², the distance traveled while powered is 0.5 * 1.7 m/s² * (41 s)² = 1,430.35 m. The final velocity when the fuel runs out is v = at = 1.7 m/s² * 41 s = 69.7 m/s. When coasting to a stop, the deceleration is due to friction: a = -0.10 * 9.8 m/s² = -0.98 m/s². Using v² = u² + 2as, where v = 0, u = 69.7 m/s, and a = -0.98 m/s², the stopping distance is s = (69.7 m/s)² / (2 * 0.98 m/s²) = 2,478.57 m. The total distance is 1,430.35 m + 2,478.57 m = 3,908.92 m, approximately 3,900 m.

Jason Takes Off Across Level Water on His Jet-Powered Skis