Solve the following :


A staircase contains three steps each $10 \mathrm{~cm}$ high and $20 \mathrm{~cm}$ wide as shown in figure. What should be the minimum horizontal velocity of a hall rolling off the uppermost plane so as to hit directly the lowest plane?


For minimum velocity ball will just be touching point $B$ If $A$ is origin then coordinates of $B(40,-20)$

$\mathrm{Y}=\mathrm{x} \tan \theta-\frac{1}{2} \frac{\mathrm{x}^{2}}{\mathrm{~g}^{\mathrm{u}^{2} \cos ^{2} \theta}}$

$-20=40 \tan 0^{\circ}-\frac{1}{2} \frac{\mathrm{g}(40)^{2}}{\mathrm{u}^{2} \cos ^{2} 0^{2}}$

$\mathrm{u}=200 \mathrm{~cm} / \mathrm{s}$

$\mathrm{u}=2 \mathrm{~m} / \mathrm{s}$


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