How Far North Does Carlos Travel in 10 Minutes?

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Homework Help Overview

The problem involves calculating the distance Carlos travels north while running at a constant velocity of 6 m/s at an angle of 25° north of east over a duration of 10 minutes. The context is rooted in kinematics and vector decomposition.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the necessity of breaking down the velocity into x and y components and how to incorporate time into kinematic equations. Questions arise regarding the appropriate equations to use and the implications of constant speed and direction on acceleration.

Discussion Status

Participants are actively exploring the problem, with some providing guidance on using kinematic equations and emphasizing the importance of understanding the motion's characteristics. There is a focus on clarifying the role of acceleration and how it relates to the equations being discussed.

Contextual Notes

There is a noted confusion regarding the application of kinematic equations and the interpretation of the problem's parameters, such as the time duration and the components of motion. Participants are encouraged to visualize the scenario to aid understanding.

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Homework Statement


Carlos runs with a velocity of = (6 m/s, 25° north of east) for 10 minutes. How far to the north of his starting position does Carlos end up?

Homework Equations





The Attempt at a Solution



I thought maybe you would solve this problem like you do for x and y components? if so...where does the 10 min. go?
 
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You do have to solve considering x and y components. The time goes in the relevant kinematics equations of motion. What are they?
 
V = Vo + at
X - Xo = volt + .5at2
v2 = vo2 + 2a(X - Xo)
X - Xo = .5(Vo + V)t
 
There is also a similar set of equations for the y direction. What should you use for the acceleration in the x and y direction?
 
i have no clue...i am confused
 
Read the problem. Draw North-South and East-West axes. Can you picture in your mind how Carlos is moving? Reread the problem. Is the Carlos' sped increasing, decreasing or staying the same? Does his direction of motion change?
 
I think his speed is staying the same... doesn't his direction stay the same as well
 
Yes, his speed and direction stay the same. This means that his velocity does not change. If his velocity does not change, what can you say about his acceleration?
 
acceleration is zero
 
  • #10
Very good. Now put zero in the place of acceleration a in the kinematic equations and write one set for the x-direction and a second set for the y-direction.
 
  • #11
which equation do I use? is there a way you could show me the first step?
 
  • #12
V = Vo + at becomes V = Vo + 0*t becomes V = Vo.

Now that you know that V = Vo, replace V in the other three equations and replace a with zero like I did above.

X - Xo = volt + .5at2
v2 = vo2 + 2a(X - Xo)
X - Xo = .5(Vo + V)t

Then repeat with y replacing x everywhere.
 

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