# A ball rolls off the top of a stairway horizontally with a velocity of 4.5m/s. Each step is 0.2m high and 0.3m wide. If g=10 m/s^2 then the ball will strike the nth step where n is equal to?

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The ball rolls off the top of a stairway horizontally with a velocity of 4.5m/s. Each step is 0.2m high and 0.3m wide.

Let the ball land on the nth step. The horizontal distance covered by the ball in the time it takes to fall n steps is 0.2*n m.

Use the formula for distance traveled in time t, d = u*t + (1/2)*a*t^2 where u is the initial velocity and a is the acceleration which is 10 m/s^2

0.2*n = 0*t + (1/2)*10*t^2

=> t^2 = 0.04*n

=> t = 0.2*sqrt n

The horizontal distance traveled in 0.2*sqrt n seconds is 0.2*sqrt n*4.5. As the ball lands on the nth stepĀ 0.2*sqrt n*4.5 = 0.3*n m.

0.2*sqrt n*4.5 = 0.3*n

=> 3 = sqrt n

=> n = 9

**The ball strikes the 9th step.**

on the first equation, how did you know that the d along y is 0.2, since you don't know yet the final position of the ball??