Question

A staircase contains three steps each $10cm$ high and $20cm$ wide. What should be the minimum horizontal velocity of the ball rolling off the uppermost plane so as to hit directly the lowest plane? (in $m{s}^{-1}$)

Answer 1

Given,

height of one step$=10cm$

Width of one step $=20cm$

The total height of the staircase $y=30cm=0.3m$

Total width of the staircase $=x=40cm=0.4m$

At minimum velocity, it will move just touching point $E$ reaching the ground $A$ is the origin of reference co-ordinate.

If $u$ is the minimum speed, $x=0.4,y=0.3,\theta =0^{\circ }$

$y=x\tan \theta -g\frac{x^2{\sec }^2\theta }{2u^2}$

where $g=10m{s}^{-2}$

$-0.3=-\frac{10\times 16\times {10}^{-2}}{2u^2}$

$u=\frac{2\sqrt{2}}{3}m{s}^{-1}$.