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

[gtn013]

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?

 

[gneill]

? 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...

 

[gtn013]

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?

 

[gneill]

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.

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.