Solving Projectiles Problem: Ball Rolls Horizontally Off Stairway

[NooDota]

Homework Statement

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

Homework Equations

The Attempt at a Solution

The book says it's the third step.

I tried, using equations:

x-x0=V0*Cos(theta0)*t

y-y0 = -1/2*g*t^2

Where x0 and y0 are both 0

x and y are both either 1 * 20.3 * 10^-2 or 2 * 20.3 * 10^-2 or 3 * 20.3 * 10^-2 etc...

And see where the time in the two equations would be equal. It wasn't the same time for the third step (3*20.3)

I got t=0.4 for the x part of the motion
and t=0.35 for the y part of the motionWhat am I doing wrong?

 

[SteamKing]

Draw a picture of the steps in profile.

Check the time it takes the ball to fall the height of the first step. In that same amount of time, will the ball travel horizontally more or less distance than the step is wide?

If it's a greater horizontal distance than the step is wide, rinse and repeat the calculation above until the ball hits a step.

 

[Chestermiller]

Homework Statement

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

Homework Equations

The Attempt at a Solution

The book says it's the third step.

I tried, using equations:

x-x0=V0*Cos(theta0)*t

y-y0 = -1/2*g*t^2

Where x0 and y0 are both 0

x and y are both either 1 * 20.3 * 10^-2 or 2 * 20.3 * 10^-2 or 3 * 20.3 * 10^-2 etc...

And see where the time in the two equations would be equal. It wasn't the same time for the third step (3*20.3)

I got t=0.4 for the x part of the motion
and t=0.35 for the y part of the motionWhat am I doing wrong?

You are assuming that the ball hits at the very end of the step. It doesn't.

 

[NooDota]

Thanks.