A staircase contains four steps each `20 cm` high and `40 cm` wide. What should be the minimum horizontal velocity of a ball rolling off the uppermost plane so as to hit directly the lowest plane ?

Explanation

To hit the lowest plane, ball must pass through the edge of the third step (as shown), so that `u` is minimum
`O` to `C`: using equation of trajectory
`y = (gx^(2))/(2u^(2))`
`x = 3b = 3 xx 0.4 = 1.2 m`
`y = 3h = 3 xx 0.2 = 0.6 m`
`0.6 = (10(1.2)^(2))/(2u^(2))`
`u^(2) = (5(1.2)^(2))/(0.6) = 12`
`u = 2sqrt(3) m//s`