Calculus question ...

[BigKev]

Ok guys, here's the question:

Two corridors whose widths are 64 units and 27 units respectively meet at a right angle. Calculate the length l of the longest rigid rod that can pass from one corridor to the other, assuming the rod remains parallel to the floor.

Picture

First, what I've done is added that dotted line to form a larger triangle ... making the sides (64+x) and (27+y) respectively.

Here's how I think I need to solve it: I need to develop a function tying this triangle together. Once I've got that I'm laughing. I'll then be able to take the derivative and set it equal to zero ... to find the MAX and MIN points ... then I'll have my maximum. The function will either a) have to be an upside-down parabola or b) have a degree higher than 3.

Any suggestions as to how to tie theta into the big picture? I think once I get on the right track to developing that function formula I'll be set but that's what I'm having a majorly hard time with. Any help and/or suggestions would be greatly appreciated ... thank you.

 

[BigKev]

no Calculus gurus on right now?

 

[Aves]

Originally posted by: BigKev
no Calculus gurus on right now?

They're all burnt out from finals/AP exams.

 

[MrCodeDude]

Everyone took the Calc AB and BC test today.. meaning everyone has since forgotten the course material

 

[simms]

I remember doing this question... but unfortunately I'm burnt out from my calc II exam. Good luck

 

[Legendary]

Find an equation that represents the hypotenuse then maximize it.
Put it this way - Length of rod = q + r
Theta = arcsin(27/r)
The angle opposite to theta (a) = 180-90-theta
sin(a) = 64/q
(q+r)² = (64+x)² + (27+y)² <--- I think maximizing that equation will help you out

I think some combination of those equations will help you out.

 

[eLiu]

Use your trig functions to put the entire equation in terms of theta. Then find your max/min. Think about what happens to that angle when the length is at max, and what happens when the length is at min. Then use trig functions (you'll have to sum the hypotenuses of the 2 triangles) to describe the lengths you need.