Max velocity up a frictionless inclined plane

AI Thread Summary
The discussion revolves around calculating the maximum velocity a puck can have while moving up a frictionless incline without hitting the upper wall of a 25 cm square air table. The calculations involve using the equations for maximum height (ymax) and maximum horizontal distance (xmax) based on the incline's angle and gravitational acceleration. The result indicates that a velocity of 5.54 m/s would lead to a ymax of 0.06 m, suggesting the puck could exceed the table's height. There is confusion about whether to set ymax to 0.01 m, as this would imply the puck wouldn't travel in the x direction. The conclusion emphasizes that any velocity above the calculated minimum would result in the puck hitting the upper wall.
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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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