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.
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??