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A staircase has 5 steps each 10 cm high ...

A staircase has 5 steps each 10 cm high and 10 cm wide. What is the minimum horizontal velocity to be given to the ball so that it hits directly the lowest plane from the top of the staircase? `(g= 10ms^(-2))`

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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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