Final answer:
To find the skier's acceleration, we calculate the gravitational force parallel to the incline, the frictional force, and then find the net force by subtracting these from the tension. Newton's second law is used to divide the net force by the skier's mass for acceleration. The direction is up the incline.
Step-by-step explanation:
The question relates to finding the magnitude and direction of the acceleration of a water skier being pulled up an incline with friction playing a role. To solve the problem, we need to apply Newton's second law of motion along with the concepts of friction, tension, gravity, and motion on an inclined plane.
First, we calculate the force of gravity acting down the incline. This force can be found using the component of the skier's weight parallel to the slope:
Fgravity = m * g * sin(Θ)
where:
- m is the mass of the skier (63 kg),
- g is the acceleration due to gravity (9.8 m/s2),
- Θ is the angle of the incline (14.0°).
Next, we calculate the force of kinetic friction using:
Ffriction = μk * N
where:
- μk is the coefficient of kinetic friction (0.27),
- N is the normal force, which is the component of the skier's weight perpendicular to the slope: N = m * g * cos(Θ).
We then determine the net force acting on the skier by subtracting the force of gravity and friction from the tension in the rope and use Newton's second law to find the acceleration:
Fnet = T - Fgravity - Ffriction
Finally, the acceleration a is found by dividing the net force by the skier's mass:
a = Fnet / m
The direction of the acceleration will be up the incline, as that is the direction of the net force.