Question

A ball released from the top of a tower travels $\frac{11}{36}$ of the height of the tower in the last second of its journey. The height of the tower is (Take $g=10m{s}^{-2})$

• A. 11 m
• B. 36 m
• C. 47 m
• D. 180 m

Answer 1

Answer: (D)

$\frac{11h}{36}=\frac{10}{2}(2n-1)$
$\frac{11}{36}\times \frac{1}{2}\times 10n^2=\frac{10}{2}(2n-1)$ or
$2n-1=\frac{11}{36}{n}^2$
or $11n^2=72n-36$ or $11n^2-72n+36=0$
or $11n^2-66n-6n+36=0$
or $11n(n-6)-6(n-6)=0$ or $(11n-6)(n-6)=0$
or $n=6$ [Rejecting fractional value]
$\therefore h=\frac{1}{2}\times 10\times 6\times 6m=180m$