Final answer:
To find the speed of a skier after 4 seconds, determine the force of gravity along the slope, subtract the kinetic friction force, and then use the net acceleration to calculate the speed using the equation v = u + at.
Step-by-step explanation:
The question involves calculating the speed of a 72 kg man on skis 4 seconds after he starts moving down a hill with a 34-degree incline and a coefficient of kinetic friction of 0.17. To find the speed, we need to determine the net force acting on the skier and then apply the equations of motion.
Firstly, we calculate the force due to gravity that acts along the slope, which is the component of the skier's weight parallel to the incline. This force can be calculated using sin(θ) × (mass × acceleration due to gravity). The acceleration due to gravity is 9.8 m/s². We then subtract the force of friction, which is the product of the coefficient of kinetic friction, the normal force (component of the skier's weight perpendicular to the incline), and cos(θ).
After finding the net force, we can find the net acceleration by dividing the net force by the mass of the skier. With the net acceleration, we can use the equation v = u + at, where 'u' is the initial velocity (0 m/s, since he starts from rest), 'a' is the net acceleration, and 't' is the time (4 seconds in this case). By plugging in the known values, we can find the skier's speed after 4 seconds.