Question:
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?
Solution:
For minimum velocity ball will just be touching point B If $A$ is origin then coordinates of $B(40,-20)$
$Y=x \tan \theta-\frac{1}{2} \frac{x^{\mathrm{a}}}{g^{u^{2} \cos ^{2} \theta}}$
$-20=40 \tan 0^{\circ}-\frac{1}{2} \frac{\mathrm{g}(40)^{2}}{\mathrm{u}^{2} \cos ^{2} 0^{\circ}}$
$\mathrm{u}=200 \mathrm{~cm} / \mathrm{s}$
$\mathrm{u}=2 \mathrm{~m} / \mathrm{s}$