The slope of the steps is 0.47. Each step has a rise of 0.14 m and a run of 0.3 m. The height of the staircase is 4.8 m.

A ball is rolled with a horizontal velocity of 1.09 m/s. Let the ball land on the nth step from the top of the staircase. The vertical distance traveled by the ball is 0.14*n and the horizontal distance traveled by the ball is 0.3*n m.

When the ball is dropped there is no change in its horizontal velocity, the vertical velocity increases due to gravitational acceleration by 9.8 m/s^2.

If the ball takes time t to land on the nth step, `1.09*t = 0.3*n` and `(1/2)*9.8*t^2 = 0.14*n`

`1.09*t = 0.3*n => t = (0.3/1.09)*n`

Substitute in `(1/2)*9.8*t^2 = 0.14*n`

=> `(1/2)*9.8*((0.3/1.09)*n)^2 = 0.14*n`

=> `4.9*(0.3/1.09)^2*n = 0.14`

=> `n = (0.14/4.9)*(1.09/0.3)^2`

=> `n ~~ 0.377`

**The ball falls on the next step from which it is rolled off.**

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