Question

A ball rolling off the top of a staircase of each step with height $H$ and width $W$, with an initial velocity $U$ will just hit $n^{th}$ step. If $H=20cm$, $W=30cm$, $U=18km/h$, then $n$ is equal to $(takeg=10m/s^2)$:

• A. $11.1$
• B. $6.5$
• C. $8.3$
• D. $12.8$

Answer 1

The correct option is A $11.1$

$n^{th}step$
$Height=nH$
$Range=nW$
${\upsilon }_n=18km/hr=5m/sec$
$nW=uh\times t$
$t=\frac{nW}{{\upsilon }_n}=\frac{nW}{5}sec$
${\upsilon }_v=0;s_v=nH$
$nH=0+\frac{1}{2}g{t}^2$
$nH=\frac{1}{2}\times g\times {\left(\frac{nW}{5}\right)}^2$
$\Rightarrow \frac{\cdot 2\times 2}{10}=n\times \frac{(\cdot 3)(\cdot 3)}{25}$
$\Rightarrow n=\frac{\cdot 2\times 2\times 25}{10\times \cdot 3\times \cdot 3}=11\cdot 1$