Submitted by Justabitwearden on Sun, 03/19/2017 - 14:23
Forums:
I am currently stuck on part (i). I have considered that for the maximum L there will be a position where the rod is in contact with two walls and the corner of the corridor and labelled an angle theta between the top wall and the rod. From this I have found an equation resembling first one (with theta instead of alpha and not an inequality since considering the maximum case) however I am not sure how to show that the angle also satisfies the second equation. Hints on where to go please?
You have $f(\theta) = a \,
You have $f(\theta) = a \, \mathrm{cosec} \, \theta + b \sec \theta \geq L$ for some general $\theta \in (0, \pi/2)$. Now: maximum, you get $f'(\theta) = 0$. Can you solve this equation? In particular, you label the solution to this $\alpha$ and show that it satisfies the second equation.
Did the question now, thanks!
Did the question now, thanks!
Awesome, well done!
Awesome, well done!