A ball (R=50cm) rolls slowly (v=1cm/s) to and then off the edge of a step that is 10cm high?

Question

How far from the step edge will the ball touch the lower surface?

http://tinypic.com/view.php?pic=5zpz4lt

Answer 1

Seems like a geometric problem, assuming the ball stays in contact with the upper corner of the step.
Vertical distance from the center of the ball to the corner contact point = 0.8*R
Angular distance wrt center of ball, from the bottom contact point to the corner contact point = theta = arccos(0.8)
Horizontal distance is R*sin(theta) = 30 cm.
Basically it's a 3-4-5 triangle scaled by 50/5.

Answer 2

Even if the ball were not rolling and falls of the edge its bottom would land 10cm away.

Now due to the velocity it would fall little bit further.

We need to calculate the time taken for free fall:

10cm = (1/2)*g*t^2

g = 9.8 m/s

0.1m = (1/2)*9.8*t^2

t = 0.14s

horizontal distance travelled during this time:
= 0.14*1cm/s = 0.14 cm

Now the bass will land at 10 + 0.14 = 10.14 cm