Calculate the speed of a boy at the end of the chute

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Homework Help Overview

The problem involves a boy sliding down a water chute, starting from rest, and requires the calculation of his speed at two points: the end of the chute and upon entering the water. The context includes considerations of energy principles and projectile motion.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss whether to treat the boy as a projectile at point B and explore the implications of the 30-degree angle provided in the problem. There are inquiries about the use of the work-energy principle for the calculations.

Discussion Status

The discussion is ongoing, with participants providing insights into the use of different methods, such as energy considerations and projectile motion. Some guidance has been offered regarding the treatment of the boy's motion and the relevance of angles in the calculations, but no consensus has been reached.

Contextual Notes

There are mentions of potential round-off errors in calculations and the need for precision in decimal places. The problem's constraints include neglecting friction and the specific angles involved in the motion.

Alexanddros81
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Homework Statement


14.11 A boy slides down a water chute, starting from rest a A. Neglecting friction
determine his speed (a) at the end B of the chute; and (b) on entering the water at C.

Fig P14_11.jpg


Homework Equations

The Attempt at a Solution



for (a):
Pytels_Dynamics105.jpg


for (b):

Do I have to treat the boy at B as a projectile?
 

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Alexanddros81 said:
Do I have to treat the boy at B as a projectile?
The answer is "No" if all you have to do is find the speed at C. You would if you had to find the time he sails through the air.
 
Am I using again principle of work and energy for (b)?
Why the 30deg angle is given at point B? Is it used in the calculations?
 
Alexanddros81 said:
Am I using again principle of work and energy for (b)?
Yes.
Alexanddros81 said:
Why the 30deg angle is given at point B? Is it used in the calculations?
Probably to show you that you can use energy considerations or projectile motion and get the same answer either way. Try it and see for yourself.
 
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Alexanddros81 said:
for (b):

Do I have to treat the boy at B as a projectile?
Yes, you must treat the boy as a projectile. The boy will have a horizontal velocity you calculated above and zero vertical velocity. Zero horizontal acceleration and gravity pulling downwards.

You could also do this with the work energy principle of course, if you wanted. As explained by kuruman
 
lekh2003 said:
The boy will have a horizontal velocity you calculated above and zero vertical velocity.
The launch speed as calculated by OP is 12.52 m/s. The velocity is directed at 30o above the horizontal and has both a vertical and a horizontal component.
 
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kuruman said:
The launch speed as calculated by OP is 12.52 m/s. The velocity is directed at 30o above the horizontal and has both a vertical and a horizontal component.
Oh yes, sorry. I made a mistake.
 
So here is my solution using work and energy principle:

Pytels_Dynamics107.jpg


Is this correct?
Also I used projectile motion and I got ##v_C=13.92 m/s##. I guess it is the precission in the decimal places of the numbers used for the calculations.
 

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Alexanddros81 said:
I guess it is the precission in the decimal places of the numbers used for the calculations.
I am sure it is round off errors. Also note that for part (b) you could have conserved energy directly from A to C and used ##U_{A \rightarrow C}=W(10~m)##.
 
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