Billy Bob is skiing down a 40-degree slope. Air resistance pushes backward on him with a force of 20 N. The coefficient of dynamic friction between his skis and the snow is 0.09. Billy Bob's mass is 103 kg. What is the magnitude of the resultant external forces acting on Billy Bob?

We calculate the normal force, determine the force of friction, identify components of gravity, and find out the resultant by subtracting the forces opposing Billy Bob's motion from the force causing it. Consequently, it's possible to find the magnitude of the resultant of the external forces acting on Billy Bob while he's skiing down a slope.

Explanation:

The problem here is from the domain of physics, particularly involving concepts from classical mechanics and forces. To solve this, we need to:

calculate the normal force, determine the force of friction, calculate the components of gravity parallel and perpendicular to the slope, and finally combine these resultant forces.

First, let's calculate the normal force. Normal Force (N) can be calculated using the formula: N = mgcosθ, where m=103kg (mass of Billy Bob), g approximates to 9.8 m/s^2 (acceleration due to gravity) and θ=40 degrees.

Then we determine the force of friction using the formula: f = μN, where μ=0.09 is the coefficient of kinetic friction and N is the normal force we just calculated.

For the forces of gravity, these are calculated along components parallel (F_parallel = mgsinθ) and perpendicular (F_perpendicular = mgcosθ) to the slope.

The resistance to motion that Billy Bob experiences comes from the frictional force and the component of his gravitational force that acts directly opposite to his direction of motion.

Hence the resultant force (F_resultant) is then calculated as F_resultant = F_parallel - f - Force of Air Resistance. Now substitute all the known values into this equation to calculate the resultant of the external forces that act on Billy Bob.

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