Find Final Position of Skater 3 on Lake

In summary, the problem involves three ice skaters on a frictionless lake, pushing off of each other and ending up at different positions. By breaking the problem into x and y components, we can solve for the position of the third skater and find their distance from the starting point. In this case, the third skater is located at (-12, -9) and their distance from the starting point is approximately 15 meters.
  • #1
anniecvc
28
0

Homework Statement


Three ice skaters are on a perfectly smooth frictionless lake. They are together at rest at the middle of the lake when they push off on each other. When skater #1 (m1 = 80 kg) is 6.00 meters EAST of the starting position, and skater #2 (m2 = 60 kg) is 6.00 meters NORTH of the starting position, how far away is skater #3 (m3 = 40) kg from the starting position?


My first intuition was to solve it this way:

Xcom = ((80kg)(6m)+(60kg)(6m) + (40kg)(X3))/180 kg

If I set Xcom to zero, X3 = 3m. Is it that simple?
However, I think I need to break it apart into components, but I'm still unclear about how to do this.

Please help!
 
Last edited:
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  • #2


anniecvc said:
However, I think I need to break it apart into components, but I'm still unclear about how to do this.
Yes, treat the x (East) and y (North) components separately. What are the x and y components of the position of masses #1 and #2?
 
  • #3


Xcom = ((80kg)(+6m) + [STRIKE](60kg)(0m)[/STRIKE] + (40kg)(X3))/180 kg

Ycom = ([STRIKE](80kg)(0m)[/STRIKE] + (60kg)(+6m) + (40kg)(X3))/180 kg

Where do I go from here?
 
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  • #4


anniecvc said:
Xcom = ((80kg)(+6m) + [STRIKE](60kg)(0m)[/STRIKE] + (40kg)(X3))/180 kg

Ycom = ([STRIKE](80kg)(0m)[/STRIKE] + (60kg)(+6m) + (40kg)(X3))/180 kg
Good.
Where do I go from here?

Also, I tried again by setting Xcom to zero (point of origin),
That's exactly what you're supposed to do.
and solving for it that way, got X=3m.
Show how you got that.
 
  • #5


Doc,

I didn't find X3=3m by breaking it up into components. I found X3 by setting Xcom = 0 = ((80kg)(6m)+(60kg)(6m)+(40kg)(X3))/180kg in my original format and solving for it algebraically.

But if I break it into components and set Xcom and Ycom to zero:

Xcom=0= ((80kg)(6m) + 0 + (40kg)(X3))/180
I get..Xx3= -12 m

Ycom=0=((0 + (60kg)(6m) + (40kg)(X3))/180
I get..Xy3 = -9 m

I'm missing the point.
 
  • #6


anniecvc said:
Doc,

I didn't find X3=3m by breaking it up into components. I found X3 by setting Xcom = 0 = ((80kg)(6m)+(60kg)(6m)+(40kg)(X3))/180kg in my original format and solving for it algebraically.
Your original approach is incorrect, since it mixes up the x and y coordinates.

But if I break it into components and set Xcom and Ycom to zero:

Xcom=0= ((80kg)(6m) + 0 + (40kg)(X3))/180
I get..Xx3= -12 m

Ycom=0=((0 + (60kg)(6m) + (40kg)(X3))/180
I get..Xy3 = -9 m
Good! You've just found the position coordinates of mass #3:

(X3, Y3) = (-12, -9)

I'm missing the point.
Use those coordinates to find its distance from the starting point.
 
  • #7


Thank you very much Doc!
 

1. How do you calculate the final position of the skater on the lake?

The final position of the skater on the lake can be calculated by using the formula: Final position = Initial position + (Velocity x Time). This takes into account the skater's starting position, their velocity, and the amount of time they have been skating.

2. What factors affect the final position of the skater on the lake?

The final position of the skater on the lake can be affected by various factors such as the skater's initial position, their velocity, the wind speed and direction, the friction of the ice, and any external forces acting on the skater.

3. How do you determine the velocity of the skater on the lake?

The velocity of the skater on the lake can be determined by dividing the distance traveled by the amount of time it took to travel that distance. This is represented by the formula: Velocity = Distance / Time.

4. Can the final position of the skater on the lake be accurately predicted?

While the final position of the skater on the lake can be calculated using mathematical formulas, it may not always be accurate due to the unpredictable nature of factors such as wind and external forces. However, with precise measurements and calculations, the final position of the skater can be estimated with a high degree of accuracy.

5. How can the final position of the skater on the lake be used in scientific research?

The final position of the skater on the lake can be used in various scientific studies, such as physics and biomechanics, to understand the principles of motion and the factors that affect it. It can also be used in sports science to analyze and improve the performance of athletes on ice. Additionally, the data collected from studying the final position of the skater can be used to create more accurate prediction models for future research and experiments.

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