Question

A staircase contains three steps each $10cm$ high and $20cm$ 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. $0.5m/s$
• B. $1m/s$
• C. $2m/s$
• D. $4m/s$

Answer 1

The correct option is C $2m/s$

To hit directly the lowest plane the ball has to cross the point $B$.

From $A$ to $B$, the ball has to travel to horizontal distance equal $40cmor40m$ and vertical distance of $20cmor0.2m$.

Let the time taken to reach point be $t$.

Given,

$u=0m/s$

$h=0.2m$

From the equation,

$h=ut+\frac{1}{2}g{t}^2$

we get

$0.2=0+\frac{1}{2}\times 9.8t^2$

$t^2=\frac{0.4}{9.8}$

$t^2=0.04$

$t=0.2$

Let $v$ be the horizontal velocity of ball than the horizontal distance travelled by the ball $=0.2v$

In order to clear the point $B$ it must be equal to $0.40$.

$2v=0.4$

$v=2m/s$

∴So minimum velocity required to to hit the lowest floor is $2m/s$.