The height and width of each step of a staircase are 20cm and 30cm respectively. A ball rolls off the top of a stair with horizontal velocity v and hits the fifth step. The magnitude of v is (g = 10 ms^–2)

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3 $\sqrt{5}$ ms^-1

1.5 ms^-1

1.5 $\sqrt{5}$ ms^-1

7.5 ms^-1

answer is A.

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Detailed Solution

$h = 5 \times 20 = 100 cm = 1 m$
$R = 5 \times 30 = 150 cm = 1.5 m$
$\begin{array}{l} R = u \sqrt{\frac{2 h}{g}} \Rightarrow 1.5 = V \sqrt{\frac{2 \times 1}{10}} \\ V = 1.5 \sqrt{5} {ms}^{- 1} \end{array}$

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