Question

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

• A. 0.5 m/s
• B. 1 m/s
• C. 2 m/s
• D. 4 m/s

Answer 1

The correct option is C 2 m/s


Formula for this condition is given by$n=\frac{2h{u}^2}{g{b}^2}$ where h = height of each step, b = width of step, u = horizontal velocity of projection, n = number of step.
= $\frac{2\times 0.1\times u^2}{10\times (o.2{)}^2}=3$
$u^2=\frac{30\times 0.04}{0.2}=6$
$u=\sqrt{6}=2.45m{s}^{-1}$