A stairway has a rise and run of 30 cm. What horizontal
velocity on the top stair will insure that the marble will fall down the stairway striking
each stair once? After striking the stair the marble maintains the same horizontal
velocity.
The stairway looks as shown.
For the marble to strike each stair once, it must have a maximum
velocity to ensure it striking the next step, and not overshooting.This is a projectile problem.
Draw the coordinate system with zero at the edge of the first
stem and with x positive down and y positive to the right (right-handed coordinates).
The six equations are
When x = 0.30 m, the marble is on the next step.
Any initial velocity less than or equal to 1.2 m/s will result in the marble striking
each step.
