A ball rolls off top of a staircase with a horizontal velocity `u m s^-1`. If the steps are `h` metre high and `b` mere wide, the ball will just hit the edge of `n th` step. Find the value of `n`.

Explanation

If the ball strikes the edge of `1^(st)` step, `x = b, y = h`
Second step, `x = 2b, y = 2h,……..n^(th) step, x = nb, y = nh`
`y:y = nh = (1)/(2) g t^(2) rArr t = sqrt((2 nh)/(g))`
`x: x = nb = ut`
`nb = usqrt((2 nh)/(g))`
`n^(2)b^(2) = (u^(2)(2 nh))/(g) rArr n = (2 hu^(2))/(gb^(2))`
OR
Equation of trajectory:
`y = (gx^(2))/(2u^(2))`
`n h = (g(nb)^(2))/(2u^(2)) rArr n = (2 hu^(2))/(gb^(2))`
NOTE : In the projectile motion, when the `x`- and `y`-coordinates are involved, try to use the equation of trajectory.