Question

Jason takes off from rest 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 have a thrust of 200N and a coefficient of kinetic friction on water of 0.10. Unfortunately, the skis run out of fuel after only 48s. What is Jason's top speed?

A) 81 m/s

B) 48 m/s

C) 130 m/s

D) 13 m/s

Answer 1

Coefficient of kinetic friction, μ = 0.10.

Mass of Jason and his skis is = M = 75 Kg

Weight of Jason and his skis = W = Mg = (75 Kg) (9.8 m/s²) = 735 N = Normal force given by the ground.

So, frictional force acting on him is F_friction = μ W = μ m g = 0.10 735 N = 73.5 N

This friction force acts opposite to the thrust (F_thrust = 200 N) of the skis.

So, net force action on him, F = F_thrust - F_friction = 200 N - 73.5 N = 126.5 N

Acceleration of him, a = F / M = (126.5 / 75) m/s² = 1.68666667 m/s² .

If the thrust acts for t = 48 sec, then the acceleration will act for t = 48 sec

So, from the formula v = u + at , (v is final velocity and u is initial velocity)

we can say, v = (1.68666667 48) m/s = 80.96 m/s

This is the exact amount of Jason's top speed. This speed is approximately equal to 81 m/s

So, option(a) is the correct option.