Solving Projectile Motion: What Step Does Ball Hit First?

[suspenc3]

A ball rolls horizontally off the top of a stairway with a speed of 1.52m/s. The steps are 1.52 cm high, and 20.3 cm wide, which step does the ball hit first.

I don't really know where to start, I kept trying to use the formulas..but I would always end up with two unknowns.

Can anyone point me in the right direction?

 

[El Hombre Invisible]

A ball rolls horizontally off the top of a stairway with a speed of 1.52m/s. The steps are 1.52 cm high, and 20.3 cm wide, which step does the ball hit first.
I don't really know where to start, I kept trying to use the formulas..but I would always end up with two unknowns.
Can anyone point me in the right direction?

The range of the ball is vT, where v = 1.52m/s and T is the duration: T = ROOT(2gnh)/g where h is the height of a step and n is the number of them passed. The range is also the sum of the widths of the steps passed, so:

nw = v/g x ROOT(2gnh)

where w = 20.3 x 10^-2.

Rearrange and solve for n, rounding down.

 

[El Hombre Invisible]

Sorry, I was counting steps 'across' when I said round down. You should round up for how many steps down the ball goes. Makes more sense.