Question

A channel $27m$ wide falls at a right angle into another channel $64m$ wide. The greatest length of the log that can be floated along this system of channels is

• A. 120 m
• B. 125 m
• C. 100 m
• D. 110 m

Answer 1

The correct option is B 125 m

Clearly,
The Length of the rod as function of angle $\theta$
$f\left(\theta \right)=\frac{27}{sin\theta }+\frac{64}{cos\theta }$
For maximum length, $f^{\prime }\left(\theta \right)=0$
Solving
$ta{n}^3\theta =27/64$
$tan\theta =3/4$
So length = $\frac{27}{3/5}+\frac{64}{4/5}=125$