Solving for Initial Velocity Up a Plane: A Homework Problem

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Homework Help Overview

The problem involves a carton given an initial speed of 3.0 m/s moving up a 22.0 degree incline, with questions regarding the distance traveled up the plane and the total time taken to return to the starting point, while ignoring friction.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss breaking the problem into equations related to forces acting on the carton, questioning how to express the initial velocity in the context of the incline.
  • Some participants explore the use of kinematic equations, while others express uncertainty about the necessary parameters like acceleration and time.
  • There is a mention of needing to find the acceleration in the x direction and how to relate it to the forces acting on the carton.

Discussion Status

The discussion is ongoing, with participants providing insights into the relationships between the variables involved. Some guidance has been offered regarding the use of kinematic equations and the calculation of acceleration, but there is still uncertainty about how to proceed with finding total time and distance.

Contextual Notes

Participants are working under the constraint of ignoring friction and are attempting to clarify the relationships between initial and final velocities, acceleration, and time without having complete information on all variables.

joseg707
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Homework Statement


A carton is given an initial speed of 3.0 m/s up a 22.0 degree plane. a.) How far up the plane will it go? b.) How much time elapses before it returns to its starting point? Ignore friction.

Homework Equations


F=ma


The Attempt at a Solution


I have no clue. If someone could point me in the right direction and try to explain what's going on I would very much appreciate it.
 
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I've been trying to figure it out. I know I'm supposed to break it into 2 equations, but I don't know how to express the 3.0 m/s velocity in the x equation.

[tex]\sum[/tex]Fx=mg*sin[tex]\theta[/tex]=max

[tex]\sum[/tex]Fy=FN-mg*cos[tex]\theta[/tex]=may=0

Is that right? If it is I still don't know where to go from here
 
Use the equation vf^2 = vi^2 + 2(a_x)(s).
 
But I don't know the time, nor the acceleration.
 
You have both the initial and final velocities so all you need right now is the acceleration in the x direction, which you can find by using mg = Fncos(theta) and a_x = gsin(theta).
 
Oh, ok. Now I get it. You put an (s) in the equation which threw me off. I found the distance and the time it took to reach the max point, but how do I get the total time? Should I just double the time it took to get to the highest point?
 

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