Final answer:
The magnitude of the stopping force is 562.5 N, and the direction is up the slope, opposing the skier's motion. This stopping force is known as the frictional force.
Step-by-step explanation:
To find the magnitude and direction of the stopping force on Mrs. Steward, we can use the work-energy principle, which states that the work done by all forces acting on an object is equal to the change in kinetic energy of that object. Since Mrs. Steward comes to a stop, her final kinetic energy is 0 joules. The work done by the stopping force, therefore also known as frictional force, is the product of the force and the distance over which it acts.
The initial kinetic energy (KEi) when Mrs. Steward is at the bottom of the slope is given by the equation KEi = (1/2)mv2, where m is her mass, and v is her initial speed. We can express the work done (W) by the stopping force as W = Fsd, where Fs is the magnitude of the stopping force and d is the distance over which it acts. Since this force is the only one doing work and brings the skier to a stop, the work done is equal to the initial kinetic energy but in the opposite direction (negative, because it's acting against the motion).
KEi = (1/2)mv2 = (1/2)(75 kg)(15 m/s)2 = 8437.5 J
W = -KEi because the skier comes to rest
W = Fs(15m) = -8437.5 J
Therefore, Fs = -8437.5 J / 15m = -562.5 N
The negative sign indicates that the stopping force acts in the opposite direction to the skier's motion, which is up the slope. Hence, the magnitude of the stopping force is 562.5 N, and the direction is up the slope.