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 11 s. How far has Jason traveled when he finally coasts to a stop?
While the jetski is running, the acceleration is F/m
The net thrust is F = 200-75g*0.1 = 126.5 N
Th acceleration is 126.5/75 = 1.69 m/s^2 and a maximum speed of
Vmax = 11*1.69 = 18.5 m/s is attained.
Distance travelled under power
= (1/2) at^2 = ___
Distance travelled while slowing down afterwards = (1/2)MVmax^2/(0.1 M g)
= 5 Vmax^2/g = ____
Add the two distances for the answer.
5400N
To calculate the distance Jason has traveled when he finally coasts to a stop, we need to consider the forces acting on him and apply Newton's laws of motion. We'll break down the problem into steps to make it easier to solve.
Step 1: Determine the net force acting on Jason:
The net force can be calculated using the equation F_net = F_thrust - F_friction, where F_thrust is the thrust provided by the skis and F_friction is the force of friction acting against the motion.
F_thrust = 200 N (given)
F_friction = coefficient of kinetic friction * normal force
The normal force is the force exerted by the water on the skis perpendicular to their surface. Since Jason is moving on level water, the normal force is equal to Jason's weight, which can be calculated using the equation weight = mass * gravitational acceleration.
Weight = mass * gravitational acceleration
Weight = 75 kg * 9.8 m/s^2 (standard gravitational acceleration)
Step 2: Calculate the force of friction:
F_friction = coefficient of kinetic friction * normal force
Substituting the value of the normal force, we get:
F_friction = 0.1 * Weight
Step 3: Calculate the net force:
F_net = F_thrust - F_friction
Step 4: Calculate Jason's acceleration using Newton's second law:
a = F_net / mass
Step 5: Calculate the distance traveled using the kinematic equation:
d = (0.5) * a * t^2
Let's calculate the distance:
First, calculate Jason's weight:
Weight = 75 kg * 9.8 m/s^2 = 735 N
Next, calculate the force of friction:
F_friction = 0.1 * 735 N = 73.5 N
Now, calculate the net force:
F_net = 200 N - 73.5 N = 126.5 N
Then, calculate the acceleration:
a = 126.5 N / 75 kg = 1.687 m/s^2
Finally, calculate the distance traveled:
d = 0.5 * 1.687 m/s^2 * (11 s)^2 = 100.17 m
Therefore, Jason travels approximately 100.17 meters before he coasts to a stop.