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Question
A staircase contains three steps each 10 cm high and 20 cm wide (in the following figure). What should be the minimum horizontal velocity of a ball rolling of the uppermost plane so as to hit directly the lowest plane ?
Solution
Given:
Height of one step = 10 cm
Width of one step = 20 cm
Total height of the staircase = y = 30 cm
Total width of the staircase = x = 40 cm
To directly hit the lowest plane, the ball should just touch point E.
Let point A be the origin of reference coordinate.
Let u be the minimum speed of the ball.
We have:
x = 40 cm
y = −20 cm
θ = 0°
g = 10 m/s2 = 1000 cm/s2
\[\therefore y = x\tan\theta - g\frac{x^2 \sec^2 \theta}{2 u^2}\]
\[\Rightarrow - 20 = - \frac{800000}{2 u^2}\]
\[ \Rightarrow u = 200 \text{ cm } /s = 2 \text{ m } /s\]
Thus, the minimum horizontal velocity of the ball is 2 m/s.
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