Skier down a hill- f=ma (is the QUESTION correct?)

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In summary: The correct formula is d = (u+v)/2 * t, not d = .5*a*t^2.In summary, the skier travels a total distance of 82 m before reaching the end of the hill, based on the given information.
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VidsEpic
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3rd time I'm posting in a day.

Homework Statement



A skier (68 kg) starts from rest but then begins to move
downhill with a net force of 92 N for 8.2 s. The hill levels
out for 3.5 s. On this part of the hill, the net force on the
skier is 22 N [backwards]. T/I
(a) Calculate the speed of the skier after 8.2 s.
(b) Calculate the speed of the skier at the end of the
section where the hill levels out.
(c) Calculate the total distance traveled by the skier before
coming to rest.

http://www.lakeheadschools.ca/scvi_staff/childs/Gr11_physics_web/downloadable_content/unit3/textpdf3/phys11_3_5.pdf [Broken]

Question 8 on the book in the link above ^

Homework Equations



f = ma

displacement = .5 * a * t^2

v^2 = u^2 + 2as

The Attempt at a Solution



a) a = f/m = 1.35 m/s/s * 8.2s = 11m/s (Correct according to answer key)

b) same procedure as above, simple physics, answer is 9.86 m/s, rounds to 10 m/s (Correct according to key)

c) For segment A .5*a*t^2 gives 45.5m and for segment B, v^2 = u^2 + 2as gives 32.45m,
but wait, I don't see what happens after that? The question doesn't even tell me when or if the skier comes to rest.
The answer key answer is 82m

I have 78m so far, am I missing something in the question or is there something wrong with it.
 
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VidsEpic said:
3rd time I'm posting in a day.

Homework Statement



A skier (68 kg) starts from rest but then begins to move
downhill with a net force of 92 N for 8.2 s. The hill levels
out for 3.5 s. On this part of the hill, the net force on the
skier is 22 N [backwards]. T/I
(a) Calculate the speed of the skier after 8.2 s.
(b) Calculate the speed of the skier at the end of the
section where the hill levels out.
(c) Calculate the total distance traveled by the skier before
coming to rest.

http://www.lakeheadschools.ca/scvi_staff/childs/Gr11_physics_web/downloadable_content/unit3/textpdf3/phys11_3_5.pdf [Broken]

Question 8 on the book in the link above ^

Homework Equations



f = ma

displacement = .5 * a * t^2

v^2 = u^2 + 2as

The Attempt at a Solution



a) a = f/m = 1.35 m/s/s * 8.2s = 11m/s (Correct according to answer key)

b) same procedure as above, simple physics, answer is 9.86 m/s, rounds to 10 m/s (Correct according to key)

c) For segment A .5*a*t^2 gives 45.5m and for segment B, v^2 = u^2 + 2as gives 32.45m,
but wait, I don't see what happens after that? The question doesn't even tell me when or if the skier comes to rest.
The answer key answer is 82m

I have 78m so far, am I missing something in the question or is there something wrong with it.

Yeah, this question is a little weird, in the sense that 3.5 s is not enough time for the skier to come to rest from 11 m/s, at that acceleration (on the straightaway). Furthermore, the problem doesn't tell you what happens after the level section, so on the surface it seems like you don't have enough info to answer the question.

If you ignore the bit in part c about "coming to rest" as being a mistake, and just calculate the total distance traveled on the downhill (8.2 s) and level (3.5 s) sections, you DO get 82 m. You have made a mistake in calculating the distance of the second portion (the level part).
 
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1. What is the formula for F=ma?

The formula F=ma stands for Force equals Mass times Acceleration. It is a fundamental equation in physics that describes the relationship between an object's mass, its acceleration, and the resulting force.

2. How does F=ma apply to a skier going down a hill?

When a skier is going down a hill, F=ma can be used to calculate the force of gravity acting on the skier. The mass of the skier remains constant, but as the skier accelerates down the hill, the force of gravity increases, resulting in a higher acceleration and ultimately a greater force acting on the skier.

3. What is the significance of F=ma in skiing?

F=ma is important in skiing because it helps us understand the forces at play and how they affect the skier's movement. By understanding this equation, we can better analyze and improve our skiing techniques, such as controlling our speed and making turns.

4. Can F=ma be used to calculate the skier's speed?

F=ma alone cannot be used to calculate the skier's speed. This equation only describes the relationship between force, mass, and acceleration. To calculate speed, we would need to also consider other factors such as friction, air resistance, and the skier's initial velocity.

5. Are there any limitations to using F=ma in skiing?

While F=ma is a useful tool in understanding the forces involved in skiing, it has its limitations. For example, it does not take into account external factors such as wind or the skier's technique. It also assumes a constant acceleration, which may not always be the case in real-life skiing scenarios.

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