The diagram below (not drawn to scale) shows the vertical cross section of a cylindrical drum with c

Question

The diagram below (not drawn to scale) shows the vertical cross section of a cylindrical drum with centre $O$ and radius $5$ cm. The drum is fixed at a point $B$ on the horizontal ground and a rectangular metal sheet leans on it.

Initially, the metal sheet touches the horizontal ground at point $P$ such that $PB=50$ cm and $\angle OPB=\theta $ radians. The metal sheet is moved in the direction $PB$ so that $P$ is $h$ cm closer to $B$ and $\angle OPB$ is increased by $\alpha $ radians, where $\alpha $ is small.

Using a suitable compound angle formula in MF26, show that
$h\approx \frac{505\alpha }{1+10\alpha }$.[4]
Hence express $h$ as a series in $\alpha $, up to and including the term in ${{\alpha }^{3}}$.[3]
Given that $P$ is moving towards $B$ at a rate of $0.1$ cms-1, find the rate of change of $\alpha $ when $h=1$.
[4]

Accepted Answer

(ii) ${505\left(\alpha - 10\alpha^2 + 100\alpha^3 + \dotsight)}$ (iii) ${0.000206 	ext{ radians per second}}$

2020 TJC P1 Q8

2020 TJC P1 Q8

Video Solution:

Solution:

Solution locked