Math Problem (kinda hard)
this one took me a while to solve, just curious if anybody else on basil can do it (it's not for a novice at mathematics):
4 insects land on the 4 corners of a square table. they start walking simultaneously at the same rate, each directing its motion steadily toward the insect on its right.
a) find the path of each insect.
b) if the table is 1 meter and the insects travel at 1cm / sec, how long will it take until they touch?
May 13, 2011
5 Comments • Newest first
haha, maybe i should draw a picture ... each lands on a different corner of the table, then they each face the insect that is (when looking from above) counterclockwise to them (aka to their right when they look at the center of the table) ... then they start walking towards the insect they are facing ... so they'll start going in a kinda counterclockwise spiral. they ALWAYS are moving directly towards the insect counterclockwise to them ... so their direction changes as all 4 of them are simultaneously moving.
hope that kinda cleared it up a little?
and just so too many people don't waste their time (aka you might not be capable of solving it), the way i did it required me to solve differential equations in polar coordinates with the center @ the middle of the table.
Either vector formulae or polar formulae.
Interesting question, though.
I'm gonna take a stab and say it looks a lot like Radius = e^theta. Maybe with some dilations, as well, like Radius = theta*[e^theta]
[quote=theAppleDog]If they all start at a corner, all walk the same direction (to their right), and are all walking the same speed, then they will NEVER touch because they're staying parallel to one another.[/quote]
That's assuming that they keep moving regardless if there's actually another insect to their right.
Vague wording is vague.
@Dafid01993 You're assuming that they turn to the insect on the right when the problem does not explicitly say so.
A. It depends which direction the insects are facing when they landed on the table.
B. 1 meter*(100 cm/1 meter)*(1 second/1 cm)
Woah wait, nevermind
It's late, I'm going to bed haha