Jason takes off across level water on his jet-powered skis. The combined mass of Jason and skis is 75 kg (the mass of the fuel is negligible). The skis have a thrust of 200 N and a coefficient of kinetic friction on water of 0.1. Unfortunately, the skis run out of fuel after only 38 s. How far has Jason traveled when he finally coasts to a stop?

Answer 1

F = m a
during thrust portion
200 - mu m g = m a
200 = m (mu g + a)
200 = 75 (.981 + a)
a = 1.69 m/s^2
distance under power = d = (1/2) a t^2
= (1/2)1.69 (38)^2 = 1217 meters
by then is going
a t = 1.69*38 = 64.2 m/s

while deaccelerating with zero thrust
Vi = 64.2
F = -mu m g = m a
a = -mu g = -.981
0 = 64.2 - .981 t
t = 65.5 seconds
average speed = Vi/2 = 32.1 m/s
distance = 32.2 * 65.5 = 2107 meters more coasting
total distance = 1217+2107 = 3325 meters