Finding the Path of a Ball on Tilted Triangle Table

[RyanGray]

Homework Statement

The vertices of a tilted triangle table are (0,0,9), (5,3,7), (4,7,6) and I need to determine where the a ball of mass m falls off of the table. There is no friction or outside forces. The ball is released from point (0,0,9).

2. The attempt at a solution
I'm not sure how to start.. I was thinking of breaking it into 2 components but it doesn't seem to work out. Any help would be appreciated.

 

[HallsofIvy]

While on the table, the ball will follow the vector with largest (negative) z component. You should be able to determine from that where the ball leaves the table.

 

[RyanGray]

wouldnt that vector = <4-0, 7-0, 6-9> = <4, 7, -6> ?

 

[HallsofIvy]

You are assuming that the ball will roll from vertex (0, 0, 9) to vertex (4, 7, 6)? Why? Why wouldn't it roll toward the other vertex. Or someplace in between?

If the ball rolls from (0, 0, 9) to the point (x, y, z) then it rolls along vector <x, y, z-9>. You want maximize z- 9 for (x, y, z) on the plane. What is the equation of that plane?