Differentiation appication: moving 14.5-m rod from hallway to corridor

[SKY KEUNG]

23. The figure shows part of the floor plan of a building. A corridor (vertical in the image) of width 2.4 meters meets a hall (horizontal) of width 8.2 meters at a right angle. A and B are points on the outer wall such that ABC is a straight line. Let D be the point at which the outer wall makes a right angle from the (vertical) corridor to the (horizontal) hall. Let the measure of the angle ABC be "theta".

(a) Express AB in terms of "theta".

(b) Find the minimum value (accurate to one decimal place) of AB.

(c) A metal rod 14.5 meters long is moved from the hall to the corridor. If the height of the floor is 4 meters, can the rod be carried around the corner by:

. . . .(i) pulling the rod along the floor?

. . . .(ii) lifting one end of the rod, while the other end remains on the floor?

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I have tried to solve c(i)(ii), but I can’t figure it out. Please help me. Thank you!

 

[mmm4444bot]

23. The figure shows part of the floor plan of a building. A corridor (vertical in the image) of width 2.4 meters meets a hall (horizontal) of width 8.2 meters at a right angle. A and B are points on the outer wall such that ABC is a straight line. Let D be the point at which the outer wall makes a right angle from the (vertical) corridor to the (horizontal) hall. Let the measure of the angle ABC be "theta".

(a) Express AB in terms of "theta".

(b) Find the minimum value (accurate to one decimal place) of AB.

(c) A metal rod 14.5 meters long is moved from the hall to the corridor. If the height of the floor is 4 meters, can the rod be carried around the corner by:

. . . .(i) pulling the rod along the floor?

. . . .(ii) lifting one end of the rod, while the other end remains on the floor?

---

I have tried to solve c(i)(ii), but I can’t figure it out. Please help me. Thank you!

I do not understand the meaning of "height of the floor". Do you?

 

[stapel]

I do not understand the meaning of "height of the floor". Do you?

I would take this as meaning "the height of the ceilings on this floor", so they're kinda high, at about thirteen feet. This would be the "grand entrance", I guess...?

 

[stapel]

23. The figure shows part of the floor plan of a building. A corridor (vertical in the image) of width 2.4 meters meets a hall (horizontal) of width 8.2 meters at a right angle. A and B are points on the outer wall such that ABC is a straight line. Let D be the point at which the outer wall makes a right angle from the (vertical) corridor to the (horizontal) hall. Let the measure of the angle ABC be "theta".

(a) Express AB in terms of "theta".

(b) Find the minimum value (accurate to one decimal place) of AB.

(c) A metal rod 14.5 meters long is moved from the hall to the corridor. If the height of the floor is 4 meters, can the rod be carried around the corner by:

. . . .(i) pulling the rod along the floor?

. . . .(ii) lifting one end of the rod, while the other end remains on the floor?

---

I have tried to solve c(i)(ii), but I can’t figure it out. Please help me. Thank you!

I'm glad to hear that you've successfully answered parts (a) and (b). What were your results for these?

Since you've "tried to solve" part (c), you'll have efforts that you can show us. Please reply with that info! For instance, you kind of guessed, going in, that probably the rod can't make the corner in just the two dimensions ("on the floor", or strictly horizontal to the floor) as they as in part (c-i), because otherwise they probably wouldn't have asked part (c-ii). What did you get for your answer for (c-i), using what you found for part (b)?

Adding in the information about how high is the ceiling (four meters, or a bit more than thirteen feet), what did you find as the distance from A (on the floor) to a point U (Up on the ceiling) directly above point B? Where did that information lead?

Please be complete. Thank you!