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
- 30372 Views
- Microsoft, Panasonic, I also Faced
- E-Mail Answers
Answers were Sorted based on User's Feedback
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 |
10 : 4 seconds :: ? : 6 minutes
Two sentences are given and we were required to print the common word in the two sentences. Words were delimited by space, full stop, ? , ! and , . The trick in the question was that common word should be printed only once so if ur first sentence contains two word "how" and second contains "how" then in output how should be printed only once for this u can replace each matched word in second sentence by spaces . i want a solution in C/C++ language
If the product of three consecutive int is 210,then sum of the two smaller ints is:
Consider a pile of Diamonds on a table.A thief enters and steals 1/2 of th e total quanity and then again 2 extra from the remaining. After some time a second thief enters and steals 1/2 of the remaining+2. Then 3rd thief enters and steals 1/2 of the remaining+2.Then 4th thief enters and steals 1/2 of the remaining+2.When the 5th one enters he finds 1 diamond on the table.Find out the total no. of diamonds originally on the table before the 1st thief entered.
it has 20 mixutre conatins mil and water in the ratio 3:5,replace 4 litres of mixture with 4 litres of water what is the final ratio of milk and water.
45 grinders brought @ 2215/-.transpot expense 2190/-.2760/- on octroi . Find SP/piece to make profit of 20% 2585 2225 2670 3325
In a party man & his wife ,and there r 2 son with their wives, and every son has 4 children in his family .how manyperson r in party.
Two Pencils 8 cents 5 Pencils cost ?
There are 19 horses in a stable. All but eight died. How many will be left in the stable?
A fly is there 1 feet below the ceiling right across a wall length is 30m at equal distance from both the ends. There is a spider 1 feet above floor right across the long wall eqidistant from both the ends. If the width of the room is 12m and 12m, what distance is to be travelled by the spider to catch the fly? if it takes the shortest path.
A, B ans C are three speakers. They have to speak randomly along with another 5 speakers in a function. A has to speak before B and B has to speak before C. What is the probability.
who is the vice president of india?
English 
