I just wanted to be sure if I got the answer right

1. Jenny (75 kg) goes on a ski trip. She goes down a slope that's inclined at 15*. Her drag coefficient is 0.300, the area of contact with the air is 0.750 m^2 and the air density is 1,31 kg/m^3. The coefficient of kinetic friction between the skis and the snow is of 0,185.

Jennys speed according to her distance:

from 0 to 15m/s: between 0m and 50m
from 15 to 20 m/s: between 50m and 100m
constant 20m/s: 100m to 450m
from 20m/s to 0: 450m to 500m

Questions:

a) What is the Work done by the force of air resistance?

A) I answered 0.687 J which seems very unlikely. This is how I proceeded:

I have the Force of air resistance formula:

1/2 CpAv^2

I have all of the numbers except for the velocity. So I just used the graph to calculate the total time it took Jenny to complete the slope. It gave me: 37.83 seconds. I then proceeded to divide the total length of the slope which is 500m. by 37.83s. to get her average velocity for that descent. It gave me 13.28 m/s which I then used in the air resistance formula and got 26N of air resistance against her. Then I just went with
W = J/s ---> W = 26 N / 37.83 s.
and it gave me 0.687 J.

Could this possibly be the answer or did I do something wrong?

so I was supposed to do Fres. X distance

for 1 J = 1N*m. I had mixed the previous formulas up, I had the W for watts instead of Work. So my final answer for the work of the air resistance is actually 26N*500m = 13,000 J or 13 kJ.

is that correct?

For finding Power, that's where I'll use 13kJ / 37,83 sec. right? = 343.64 watts.

To calculate the work done by the force of air resistance, you correctly used the formula: W = 1/2 CpAv^2. However, there seems to be an error in calculating the average velocity.

To find the average velocity, you divided the total distance of 500m by the total time of 37.83s, resulting in an average velocity of 13.28 m/s. However, this calculation assumes a constant velocity throughout the entire descent, which is not the case based on the given speed intervals.

To accurately calculate the average velocity, you need to consider the varying speeds at different intervals of the slope. You can break down the slope into intervals and calculate the average velocity for each interval separately.

For the first interval (0 to 15 m/s, between 0m and 50m), you can use the midpoint velocity of the interval, which is (0 + 15)/2 = 7.5 m/s. The distance for this interval is 50m.

Similarly, for the second interval (15 to 20 m/s, between 50m and 100m), the midpoint velocity is (15 + 20)/2 = 17.5 m/s, and the distance is 50m.

For the third interval (constant 20m/s, between 100m and 450m), the velocity remains constant at 20 m/s, and the distance is 350m.

For the fourth interval (20m/s to 0, between 450m and 500m), you can use the midpoint velocity again, which is (20 + 0)/2 = 10 m/s. The distance is 50m.

Now, calculate the average velocity for each interval by dividing the distance by the time taken. You can then calculate the total time taken by summing up the individual times for each interval.

Once you have the average velocity for the entire descent (or the total time taken), you can substitute it into the formula W = 1/2 CpAv^2 to calculate the work done by air resistance.