Question

Jason takes off across level water on his jet-powered skis. The combined mass of Jason and his skis is 75kg (the mass of the 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 seconds. How far from his starting point has Jason traveled when he finally coasts to a stop?

Correct answer: 3900m   Show with steps how to solve, thanks homie

Answer 1

F(=200) - Ff(= 0.1*75g) = m*a

a = (200-7.5g)/75 = 1.69 m/s^2, jet ski acceleration

d1 = 1/2 at^2

d1 = (1/2)(1.69)*41^2 = 1420.5 m, travels this far before fuel spent

Vf^2 = Vo^2 + 2a(d1)

Vf = sqrt(0+2*(1.69)*(1420.5))= 69.3 m/s, attains a final velocity

d = d1 + d2

a = -Ff/m = 0.1*75g/75 = -0.981 m/s^2, deceleration due to friction while coasting (assume constant)

Vf^2 = Vo^2 - 2a(d2), where its Vo, is the final velocity achieved when fuel spent

Vf = 0 = 69.3^2 - 2(0.981)(d2), it comes to rest when Vf=0

d2 = 69.3^2/(2*0.981) = 2447.75 m by coasting this far

d = 1420.5 + 2447.75 = 3868.25 m total travel distance