Max velocity up a frictionless inclined plane

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SUMMARY

The maximum velocity of a puck on a frictionless inclined plane, given a rise of 1 cm over a 25 cm distance, is calculated to be 5.54 m/s. This velocity ensures that the puck does not hit the upper wall of the air table. The equations used include ymax = (V^2sin(θ))/(2g) and xmax = 2V^2sin(θ)cos(θ)/g, with θ calculated as 2.29 degrees. The discussion clarifies that any velocity greater than this maximum will result in the puck exceeding the height of the table.

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Homework Statement


The air table is approximately 25 cm square. If the incline has a rise of 1cm over that distance, what is the maximum velocity up the slope that a puck may have and not hit the upper wall


Homework Equations


ymax = (V^2sin(θ))/(2g)
xmax = 2V^2sin(θ)cos(θ)/g

The Attempt at a Solution



0.25 = (2 v^2 sin(2.29) cos(2.29))/9.81

V = 5.54

then I took my result substituted it into the y max equation.

ymax = ((5.54^2)*sin(2.29))/(2*9.81) = .06 M

Does this mean that if the puck was launched at that velocity, it would go off the end of the table? Should first be setting ymax = .01? If I do that, it does not seem that the puck would go anywhere in the x direction.
 
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I think you mean the minimum velocity the puck should have. Because any velocity beyond the minimum velocity would be enough for the puck to hit the top portion of the table..
 

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