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 fuel is negligible)
the skis produce a forward thrust of 200n and have a coefficient of kinetic friction with water of 0.10
unfortunately, the skis run out of fuel after only 94s
how far from his starting point has jason traveled when he finally coasts to a stop?

I would draw you a force diagram to help with the explanation, but I don't know how to put a picture up. Therefore I'll just try my best without.

The problem comes in two phases. The first is when the jets are operating. Here the forward horizontal force is 200N, and there is a frictional force Fr acting in antiparallel (the opposite direction).

Forces are balanced in the vertical sense, since the skier neither takes off from or sinks into the water. Therefore his normal reaction force, R, is equal to his weight force. Since W = mg, we see that R = mg.

Next, use the formula Fr = uR, where u is the coefficient of kinetic friction, to calculate Fr = umg.

This makes the resultant horizontal force in phase 1 equal to (200 - umg)N. By Newton's Second Law of Motion, and with the slightly callous assumption that the combined mass of him and his apparatus is constant, F = ma. Therefore a = F/m = ((200 - umg)/m) ms^-1.

Now we can use the equations of motion for constant acceleration to calculate both the skier's velocity and displacement at t = 94s.

S = ?
U = 0ms^-1
V = ?
a = ((200 - umg)/m) ms^-2
t = 94s

Using S = Ut + 0.5at^2:

S = (0)(94) + (0.5)((200-umg)/m)(94^2) =