Crooked Air Hickey Table

[nateshoe]

1. The problem statement, all variables and given/known data

A physics student playing with an air hockey table (a frictionless surface) finds that if she gives the puck a velocity of 3.82 m/s along the length ( 1.65 m) of the table at one end, by the time it has reached the other end the puck has drifted a distance 2.47 cm to the right but still has a velocity component along the length of 3.82 m/s. She concludes correctly that the table is not level and correctly calculates its inclination from the above information.

2. Relevant equations



3. The attempt at a solution
I don't even know where to start! It has to be solved in three dimensions and I'm having trouble setting it up.

[weatherhead]

this problem could be a lot simpler than you first think. At first sight, admittedly, it looks like a 3d vector problem. However, given that there is no friction, and the only force affecting the motion is the weight, it is in fact a 2 - dimensional problem. The vertical plane (with weight "visible") is where the mechanics goes on, and the motion along the table is useful for one thing only - calculating the transit time. There is no force in this direction.

Try drawing a diagram representing the puck as a particle and the table as a line at an angle to the vertical. The only force acting is weight. Draw this force on. Now, try and derive an equation for the acceleration "sideways" accross the table. Bearing in mind about what I said earlier about using the other direction to calculate the time, you should easily be able to just use kinematic equations of motion, and it's a fairly simple problem. Good luck

[weatherhead]

by the way, the answer I get for this problem is quite a small angle, which is probably intuitively what one would expect!

[nateshoe]

I got it figured out, thanks!