Question

A ball rolls of the top of a stairway with horizontal velocity of magnitude $1.8m{s}^{-1}$. The steps are $0.20$ high and $0.20m$ wide. Which step will the ball his first? $(g=10m{s}^{-2})$.

Answer 1

$x=0.2m,nx=\frac{1}{2}g{t}^2,nx>ut\Rightarrow n^2{x}^2>u^2{t}^2$

$n^2{x}^2>\frac{u^{2}nx}{g}$

$n>\frac{2u^2}{gx}\Rightarrow n>\frac{2(1.8{)}^2}{2\times 0.2}$

$n>3.24$

and $(n-1)x=drac12g{t}_1^2$

$\Rightarrow n{t}_1>(n-1)x$

$u^2{t}^2>(n-1{)}^2{x}^2$

$\Rightarrow \frac{u^{2}2(n-1)x}{g}>(n-1{)}^2{x}^2$

$\Rightarrow \frac{2u^2}{gx}>n-1$

$\Rightarrow n-1<3.24$

$n<4.24$