Mechanics- general motion in a straight line.

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Discussion Overview

The discussion revolves around a mechanics problem involving the motion of a ball bearing fired vertically upwards and its subsequent fall through a tub of butter. Participants are addressing the calculations related to the time of rest and the distance traveled, specifically focusing on the third part of the problem regarding the time taken to fall back to the original position.

Discussion Character

  • Homework-related

Main Points Raised

  • One participant presents the problem statement, including the equations for upward and downward velocities of the ball bearing.
  • Another participant expresses confusion about how to calculate the time taken for the ball bearing to fall back to its original position after it comes to rest.
  • Several participants suggest using integration to solve for the time in the downward motion, specifically referencing the integral of the downward velocity equation.
  • There are repeated requests for clarity on the problem statement, indicating that the initial image may not have been clear.

Areas of Agreement / Disagreement

Participants generally agree on the approach of using integration to solve the problem, but there is no consensus on the specific calculations or the interpretation of part (c) of the problem.

Contextual Notes

Some assumptions about the initial conditions and the definitions of variables may be missing, which could affect the clarity of the problem. The integration steps and limits are not fully resolved in the discussion.

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20210608_181630.jpg

I calculated q(a)=1s
q(b)=7cm
I don't understand q(c)
 
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Fix the image to make it readable or type out the problem statement yourself.
 
skeeter said:
Fix the image to make it readable or type out the problem statement yourself.
Apologies.
A ball bearing is fired vertically upwards in a straight line through a tub of butter. The upward velocity of the ball bearing is given by v=13-10t-3t^2 cm/s, where t is the time from when it was fired upwards.
a) Find the time when the ball bearing comes momentarily to rest
b) Find how far the ball bearing has traveled upwards at this time

The ball bearing then falls downwards through the hole it has made in the butter. The downward velocity of the ball bearing is given by v= 10T cm/s, where T is the time from when it was momentarily at rest.
C) Find the time that the ball bearing takes ( from when it was momentarily at rest) to fall to its original position.
Iam not understand how to calculate (c)
 
$\displaystyle \int_0^t 10T \, dT = 7$

solve for $t$
 
skeeter said:
$\displaystyle \int_0^t 10T \, dT = 7$

solve for $t$
Thank you very much!
 

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