A group of high level managers is given an exercise in which they must measure the height of the flagpole at the front of their building. They take a ladder and a tape measure but have a hard time setting it up, not falling off it and generally struggling to get anywhere near completing the task. An engineer walks by and realises what they’re trying. He pulls the flagpole out of the ground and lays it flat. Easily measuring from one end to the other, he hands the measurement to the team leader and walks away. “Typical engineer,” says the leader, “we’re looking for the height and he gives us the length.”
That was a joke. This isn’t. A ladder is leaning on a wall (which is perpendicular to the floor). It’s initially at rest. Now it starts to slide down (there’s no friction). Prove that the ladder loses contact with the wall when it slides down exactly 1/3rd of its original height.
(The problem concerned a goat tied by a 60 metre rope to a corner of a square house with 30 metre sides and you had to find out the number of square metres it could graze. Also, where would it have to be tied for maximum and minimum grazing.)
(a) Maximum area that the goat can graze is three quadrants of radius 60 and two quadrants of radius 30, which is (0.75*pi*60*60) + (0.5*pi*30*30) = 3150*pi = 9896 square metres. (b) For minimum area, it is to be tied at the midpoint of a side. Area in that case would be a semicircle of radius 60, two quadrants of radius 45, and two quadrants of radius 15, which is (0.5*pi*60*60) + (0.5*pi*45*45) + (0.5*pi*15*15) = 2925*pi = 9189 square metres. -- K Sathyadev, firstname.lastname@example.org
The maximum area the goat can graze is when it is tied to a corner of the house. Grazing area is then approximately is 9896 sq metres. The minimum area it can graze when the goat is tied to middle of one side of the house. Area that it can graze is then approximately is 9189.2 sq meters. -- Ravi Nidugondi, email@example.com
(The other problem was: ”In micro or zero gravity, can one get dizzy after spinning and stopping?”)
Humans rely on the vestibular system for balance and attitude. In a zero gravity or micro-gravity environment, this system does not work since the fluids in it do not move correctly in the absence of significant gravitational force. But they do still move because of inertia. Etc, etc, etc. As a result of these factors, everyone has motion sickness in zero or micro-gravity environment, based on the vestibular system signs that we are moving but we can’t see it. -- Dr K N Murty, firstname.lastname@example.org
(Sorry Doc -- and about two dozen others who also wrote in saying the same thing but, illogical as it sounds, you do NOT get dizzy in micro or zero gravity as the British astronaut Tim Peake recently proved during his stint on the International Space Station. See an ultracool video at: https://www.youtube.com/watch?v=2Lz5UeROyXM -- MS)
(However as to why skaters and ballet dancers don’t get dizzy either, as the third puzzle wanted to know, there’s another answer)
Ballet dancers and ice skaters do not get dizzy after fast spinning because they use the two techniques of spotting and vestibular therapy. In spotting, these artists keep their head in one position for as long as possible by focusing on one thing and then rotating it around quickly back to another fixed position. In vestibular therapy, they make use of brain plasticity over years of training to desensitise themselves to the propensity towards vertigo. -- Shashi Shekher Thakur, email@example.com
As per Winter Olympic Gold figure skater Evan Lysacek, ice skaters do get dizzy but get used to it and their bodies learn to build a tolerance for it. -- Abhay Prakash, firstname.lastname@example.org
BUT GOOGLE THIS NOW
1. If 0313 = 1, 7662 = 2, 3213 = 0, 1111 = 0, 6666 = 4, 9881 = 5, 6855 = 3, 7756 = 1, 1012 = 1, 5555 = 0 then what does 2581 = ?
2. Dilip, email@example.com writes: “The answer given for the ice and water level problem is wrong. Ice at 0 degrees has a lower density than water at 0 degrees. So the volume will come down and not stay the same.” While Dilip, firstname.lastname@example.org says: “How stupid you and some readers are! Water is not a liquid at zero degrees. It’s ice.”
Sharma is a scriptwriter and former editor of Science Today magazine.