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There are four dogs/ants/people at four corners of a square
of unit distance. At the same instant all of them start
running with unit speed towards the person on their
clockwise direction and will always run towards that target.
How long does it take for them to meet and where?
- 8 Answers
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Answer / md abdul aziz
They will meet at the center of the square...as the
direction vector of all the ants/people change according to
the first person.
The independent path of each person taken will be spiral in
nature.
| Is This Answer Correct ? | 50 Yes | 6 No |
Answer / kushank poddar
they will meet at the centre.
if we look at any two of them we find that :-
O------>
^ v=1unit/sec
| 1 unit
|
|
O
the other particle is moving perpendicular to the
approaching particle and hence its component of velocity
along the line joining the 2 points is 0.
hence,
time taken = 1unit/ {1unit/sec} = 1sec.
anddistance travelled by each particle is 1unit.
:)
thanks.
| Is This Answer Correct ? | 23 Yes | 2 No |
Answer / nikhra
They will meet at the center of the square after unit time,
they will travel unit distance.
At any moment of time dogs will be at the corner of another
square with smaller size and same center, size of square
will decrease with time and finally they will meet at
center.
At any moment of time their speed toward center will be
1*cos(45) = 1/√2, and radial distance is √2, so they will
meet after √2/ (1/√2) = 1 unit time and will travel unit
distance.
| Is This Answer Correct ? | 24 Yes | 11 No |
Answer / venkat
Sorry I goofed up on the distance traveled in my above post
and also the formatting of the message. moderator, please
feel free to correct the format.
It looks like my estimate about the arc close to the diagonal
is wrong and the path is more spiral
Here is a link that I came across that gives the graphic simulation
of the spiral path for the problem at hand.
http://sohaib-khan.blogspot.com/2011/09/four-ants-at-corner-of-square.html
The distance travelled was mentioned in the same link as 1 unit
| Is This Answer Correct ? | 0 Yes | 0 No |
Answer / venkat
answer # 3 is almost correct. they will meet at the center however the time they would take according to my calculation is not 1 unit of time but less than 1 unit of time [approx 0.78 unit of time]. the reason being since all of the four are moving tracing arcs toward the center of the square, the distance of the arc is definitely less than 1 unit [little more than half the diagonal distance, half the diagonal distance is about = 0.707 unit]. the question says speed and not velocity. speed is distance traversed / time taken to cover the distance. Here distance is the length of the arc [0.78 unit] to be precise and not even half the diagonal distance [0.70 unit], leave alone the initial distance [1 unit] between the two people. arc length that I got was using this formula: (2 x pi x 0.5) / 4 = 0.78. Further 1 unit speed = 0.78 unit / time and it follows time = 0.78 unit of time.
| Is This Answer Correct ? | 1 Yes | 2 No |
Answer / kevin
Answer number 4 is ALMOST correct. Since it's a unit
square, r will actually equal 1/2, so the answer should be pi/4.
| Is This Answer Correct ? | 6 Yes | 9 No |
Answer / tarun
The reason previous answer is wrong is because at any given
point of time they are not moving along the diagonal of the
square. They end up traversing a quarter-circular arc - this
can be verified by looking at the tangents on the four
circular arcs at any given point of time and they will show
how each ant is moving instantaneously in a straight line in
the direction of its neighbor. Therefore the total distance
covered is 1/4(2*pi*r) where r=1, or pi/2, and so the total
time taken is also pi/2 units.
| Is This Answer Correct ? | 3 Yes | 23 No |
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