Solve Staircase Projectile Problem: Find the First Step Hit

[asdf1]

A ball rolls out from the top of the stair case, with a horizontal velocity of 5 ft/s. Each step is 8 inches wide and 8 inches long. Which step will the ball hit first?

My problem:
I'm stuck on how to handle the problem. Where do you start thinking?

 

[PPonte]

You could try trial and error.
First, see if the ball will hit the first step.
If not, then see if the ball will hit the second step.
If not, then see if the ball will hit the third step.
...

Useful formulas:

$$t_{falling} = \sqrt{\frac{2h}{g}$$

$$x_{max} = v_0\sqrt{\frac{2h}{g}$$

Maybe there is a better method to solve the exercise. But that's the only one I see. Hope it helps!

 

[0rthodontist]

See when the ball drops below the line joining the edges of the steps. It will hit the step that is immediately below the point where it crosses that line.

 

[Office_Shredder]

See when the ball drops below the line joining the edges of the steps. It will hit the step that is immediately below the point where it crosses that line.

Keep in mind the ball falls in a parabolic motion

 

[0rthodontist]

http://img148.imageshack.us/img148/580/stepssy0.png

 

[asdf1]

wow... thanks! how'd you think of that?

 

[leo_thunderbird]

let it fall on the nth step
v along x=5cos theta
n*8(length of the step)=vcostheta*t
here theta=0(thrown along the x axis)
similarly proceed in y direction and finally equate t in both the eqn

 

[asdf1]

thank you very much!