A 55 kg skier is going down a slope with an angle of 47 degrees. Mk= 0.15. How fast is he going after 6 seconds?

To find the speed of the skier after 6 seconds, we can use the principles of Newton's second law and the laws of motion.

First, let's calculate the gravitational force acting on the skier:

Gravitational force (Fg) = mass (m) * acceleration due to gravity (g)
= 55 kg * 9.8 m/s^2
≈ 539 N

Next, let's determine the component of the gravitational force acting down the slope (Fg parallel to the slope) and perpendicular to the slope (Fg perpendicular to the slope):

Fg parallel to the slope = Fg * sin(θ)
= 539 N * sin(47°)
≈ 365.7 N

Fg perpendicular to the slope = Fg * cos(θ)
= 539 N * cos(47°)
≈ 378.1 N

Now, let's calculate the net force (F net) acting on the skier parallel to the slope:

F net = Fg parallel to the slope - frictional force (Ff)
= Fg parallel to the slope - coefficient of kinetic friction (μk) * Fg perpendicular to the slope
= 365.7 N - 0.15 * 378.1 N
≈ 365.7 N - 56.7 N
≈ 309 N

Next, we need to determine the acceleration (a) of the skier:

F net = m * a
309 N = 55 kg * a
a ≈ 5.62 m/s²

Finally, we can calculate the final velocity (v) of the skier after 6 seconds using the kinematic equation:

v = u + a * t

where:
u = initial velocity (assumed to be 0 m/s since it wasn't given)
a = acceleration (5.62 m/s²)
t = time (6 seconds)

v = 0 + 5.62 m/s² * 6 s
v ≈ 33.72 m/s

Therefore, the skier is going approximately 33.72 m/s after 6 seconds.