# A Staircase contains three steps each 10cm high and 20cm wide.What should be the minimum horizontal velocity of a ball rolling off the uppermost plane so as to hit directly the lowest plane.

### Asked by JAIBHARGAVA200 | 30th Oct, 2014, 07:56: PM

Expert Answer:

### Let h be the height and w be the width of each step.
Let O be the uppermost plane and A be the lowermost plane.
Let the ball roll from the uppermost plane O with a horizontal velocity 'v' .Here the vertical velocity (velocity in the y direction will be 0)
If 't' is the time taken by the ball to reach the lowest plane A and 'x' the horizontal range, then we have:
x = v t
t = x /v ---------------------(1)
Here the horizontal range of the ball lies between 2w and 3 w, or we can say that the horizontal range (x) of the ball will be greater than 2w.
Given h = 10 cm =0.10 m,
w = 20 cm =0.20 m
i.e. x ≥ 2w
x ≥ 2×0.20m
x≥ 0.40 m
The vertical height, through which the ball travels from the plane O to plane A = 2h
From the equation of motion, s=ut+(1/2) gt^{2}
Here u =o for vertical motion so:
2h = (1/2)gt^{2 }
From (1) and (2) we get that
**So the minimum horizontal velocity ****of a ball rolling off from the uppermost plane(O) so as to hit directly the lowest plane(A) of the staircase = 2 m/s**. Further for the ball to roll from the point O to reach the ground level the horizontal velocity should be greater than 2 m/s.

^{2}

^{2 }

**So the minimum horizontal velocity**

**of a ball rolling off from the uppermost plane(O) so as to hit directly the lowest plane(A) of the staircase = 2 m/s**. Further for the ball to roll from the point O to reach the ground level the horizontal velocity should be greater than 2 m/s.

### Answered by Jyothi Nair | 31st Oct, 2014, 12:54: PM

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