A snowboarder of mass 74.4 kg (including gear and clothing), starting with a speed of 5.0 m/s, slides down a slope at an angle è = 37.1° with the horizontal. The coefficient of kinetic friction is 0.116. What is the net work done on the snowboarder in the first 6.02 s of descent

Fs = 74.2kg * 9.8 = 727.2N @ 37.1deg = Force of snowboarder.

Fp = 727.2sin37.1 = 438.6N = Force parallel to plane.

Fv = 727.2cos37.1 = 580N = Force perpendicular to plane.

Ff = u*Fv = 0.116 * 580 = 67.3N = Force of friction.

Fn = Fp - Ff = 438.6 - 67.3 = 371.3N = Net force acting on snowboarder.

a = Fn/m = 371.7 / 74.2 = 5m/s^2.

d = Vo*t +0.5at^2,
d = 5*6.02 + 0.5 * 5 * (6.02)^2,
d = 30.1 + 90.6 = 120.7m.

W = Fn * d = 371.3 * 120.7 = 44816 Joules.

To find the net work done on the snowboarder, we need to calculate the work done by different forces acting on the snowboarder.

1. Calculate the gravitational force (Fg) pulling the snowboarder down the slope:
Fg = m * g * sin(θ)
= 74.4 kg * 9.8 m/s² * sin(37.1°)
≈ 431.64 N

2. Calculate the normal force (Fn) perpendicular to the slope:
Fn = m * g * cos(θ)
= 74.4 kg * 9.8 m/s² * cos(37.1°)
≈ 592.60 N

3. Calculate the force of kinetic friction (Fk) opposing the motion of the snowboarder:
Fk = μ * Fn
= 0.116 * 592.60 N
≈ 68.61 N

4. Determine the total distance traveled by the snowboarder in the first 6.02 s using the formula:
d = ut + (1/2) * at²
= 5.0 m/s * 6.02 s + (1/2) * 0 * (6.02 s)²
= 30.10 m

5. Calculate the work done by the gravitational force (Wg) along the slope:
Wg = Fg * d * cos(θ)
= 431.64 N * 30.10 m * cos(37.1°)
≈ 12,940.69 J

6. Calculate the work done by the force of kinetic friction (Wk) opposing the motion:
Wk = Fk * d
= 68.61 N * 30.10 m
≈ 2,064.59 J

7. Calculate the net work done by subtracting the work done by friction from the work done by gravity:
Net work done = Wg - Wk
= 12,940.69 J - 2,064.59 J
≈ 10,876.10 J

Therefore, the net work done on the snowboarder in the first 6.02 seconds of descent is approximately 10,876.10 Joules.

To find the net work done on the snowboarder, we need to calculate the change in kinetic energy.

The formula for work is given by:
Work = Force × Distance × cos(θ)

In this case, the force is the force of kinetic friction, which can be calculated using:
Force of kinetic friction = coefficient of kinetic friction × Normal force

The normal force is the force exerted by the surface perpendicular to it, which in this case is equal to the gravitational force acting on the snowboarder:
Normal force = Mass × Gravity

Since the snowboarder is sliding down the slope, the component of the gravitational force acting parallel to the slope generates the force of kinetic friction. The gravitational force can be calculated as:
Gravitational force = Mass × Gravitational acceleration × sin(θ)

Now we can calculate the net work done on the snowboarder.

First, calculate the gravitational force:
Gravitational force = 74.4 kg × 9.8 m/s^2 × sin(37.1°)

Next, calculate the normal force:
Normal force = 74.4 kg × 9.8 m/s^2

Then, calculate the force of kinetic friction:
Force of kinetic friction = 0.116 × Normal force

Now we can calculate the work done on the snowboarder by the force of kinetic friction:
Work = Force of kinetic friction × Distance × cos(θ)

The distance can be calculated using the formula for horizontal displacement:
Distance = Initial velocity × time + 0.5 × acceleration × time^2

Since the snowboarder is moving horizontally, the horizontal acceleration can be calculated as:
Acceleration = Gravitational acceleration × sin(θ)

Substituting the given values, we can calculate the distance.

Finally, substitute all the values into the work formula to find the net work done on the snowboarder in the first 6.02 s of descent.