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A staircase contains three steps each 10...

A staircase contains three steps each `10 cm high and 20 cm` wide. What should be the minimum horizontal velocity of the ball rolling off the uppermost plane so as to hit directly the lowest plane ? `("in" m s^-1)`.
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Text Solution

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If it is to hit the lowest plane and velocity to be minimum, then it must just avoid to hit the edge of 4th step. Thus, the trajectory of the ball should be such as shown in figure. Time taken to travel a vertical distance of 40 cm from point A to B is

`t= sqrt((2h)/(g))= sqrt((2xx0.4)/(10))=0.2 sqrt(2) s`
Since the horizontal distance between A and B is 40 cm and the ball covered it in `0.2 sqrt(s)`
horizontal velocity of ball is `v=(0.4)/(0.2 sqrt(2))= sqrt(2) ms^(-1)`
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