How High Do Crossing Stones Meet When Thrown from Opposite Ends of a Cliff?

AI Thread Summary
Two stones are thrown from a cliff simultaneously, one upward and the other downward, both at 9.00 m/s, from a height of 6.00 m. The key to solving the problem lies in correctly applying the equations of motion while maintaining a consistent coordinate system for both stones. The discussion emphasizes that using different coordinate systems for each stone can lead to incorrect results, as all measurements must reference the same system. The importance of sign conventions in physics calculations is highlighted, as a simple error can complicate the solution process. Ultimately, clarity in defining the coordinate system is crucial for accurately determining where the stones cross paths.
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Homework Statement


Two stones are thrown simultaneously, one straight upward from the base of a cliff and the other straight downward from the top of the cliff. The height of the cliff is 6.00m. The stones are thrown with the same speed of 9.00 m/s. Find the location (above the base of the cliff) of the point where the stones cross paths.


Homework Equations



x = vot+ (1/2)at^2
vf=vo + at
vf^2 = vo^2 + 2ax

The Attempt at a Solution



x1 = vo1t + 1/2(-g)t^2; x2 = vo2t + 1/2(-g)t^2;
x1 + x2 = vo1t +vo2t - gt^2 = xtotal
? does vo1 = 9 m/s while vo2= -9 m/s? OR vo1 and vo2 = 9 m/s? If the latter, why?
 
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gtn013 said:
? does vo1 = 9 m/s while vo2= -9 m/s? OR vo1 and vo2 = 9 m/s? If the latter, why?

The sign on the velocities depends upon your choice of coordinate system. Since you've specified -g for the acceleration due to gravity in your equations, it would seem that you've selected + for upwards and - for downwards... :wink:
 
Does each stone use the same coordinate system then? Could they use different coordinates where for stone 1 thrown downwards: vo1 = 9 and a = g while stone 2 thrown upwards is: vo2 = 9 and a = -g?
 
gtn013 said:
Does each stone use the same coordinate system then? Could they use different coordinates where for stone 1 thrown downwards: vo1 = 9 and a = g while stone 2 thrown upwards is: vo2 = 9 and a = -g?

You may use as many different coordinate systems as you like, unless of course you wish to get correct answers. :wink:

It is vitally important when analyzing physics problems that all measurement values be referenced to the same coordinate system! Otherwise any mathematical comparison or operations amongst the measurements will be meaningless.

You might be able to keep the relationships between a few items straight in your head for simple problems and make the appropriate sign corrections as you go, but it's asking for trouble... a simple sign slip in the middle of a long calculation can be a devil to track down.
 

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