Question

A ball rolls
off the top of a stairway horizontally with a velocity of 4.5 m s¯¹. 
Each step is 0.2 m high and 0.3 m wide. If g is 10 m s ¯² then the ball
will strike the edge of nth step where n is equal to ……………………………

Answer 1

Let It strikes nth step edge.
So 4.5*t=0.3*n  => t=n/15

1/2 * g * t^2 = 0.2*n

5 * n^2/225 = 0.2*n

n=9

Answer 2

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 step 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.

Hope it helps !