Cullen Banks

2023-03-03

A small block slides, without friction, down an inclined plane starting from rest. Let ${S}_{n}$ be the distance travelled from time t=(n-1) to t=n. If $\frac{{S}_{n}}{{S}_{n+1}}$ is found to be 5/7, then value of n is?

Elliot Watson

Distance travelled in t sec $={S}_{t}$
$\therefore {S}_{t}=u+at-a/2$
as u=0
$\frac{{S}_{n}}{{S}_{n+1}}=\frac{an-a/2}{a\left(n+1\right)-a/2}=\frac{a\left(2n-1\right)×2}{2a\left(2n+1\right)}\phantom{\rule{0ex}{0ex}}=\frac{2n-1}{2n+1}=\frac{5}{7}\phantom{\rule{0ex}{0ex}}⇒14-7=10n+5\phantom{\rule{0ex}{0ex}}⇒4n=12\phantom{\rule{0ex}{0ex}}⇒n=3$

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