Solve it - Question 8

Dear All

One of my student (now not studying in CRPF School)shared this math problem with me. Let us all try together to solve it.
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The question is as follows:

Let two cyclists A and B start from a point 100kms apart from each other with the speed of 10kms towards each other. As they start a bee takes off from the nose of a cyclist a and heads towards B's nose.It turns back and heads towards A's nose.It continues this back and forth movement till it gets squashed between doing this how much total distance does the bee covers? Given speed of bee is 20 km/hr.

Well, he also shared this piece of information. Hope all the readers will like it...

Borrow a necklace from a shop and hold it up in the air by its two ends at the same level so that it hangs downwards.The necklace assumes the shape of a curve.This curve is named as catenoid.
the problem posed by jacob bernoulli was to find the equation for the curve.
the curve is not a parabola.
it was found that
y=a(e^(x/a) + e^(-x/a))/2 + b
a and b are constants
a =depends on physicsal characteristics e.g. density how far ends were held .
b =the placement on x axis which can be 0 also.
Among all possible shapes that hanging string can assume ,catenary is one for which potential energy of string is minimised .
centre of gravity at this shape of string is at the lowest.
Dip the two identical circular hoops of wire into a soap solution in contact with one another along their entire circumference.Let the hoops be pulled out of soap solution and drawn apart carefully.Soap solution produce s a soap film connecting the two hoops, and the shape assumed by the film is a catenoid.The soap film the shape which minimises the total potential energy.


  1. well, i think that speed of bee must be known to us.
    Two cyclist will take total of five hours to meet with other. so, to tal distance travelled by bee is equal to speed x 5 km

  2. Yes, there was this similar question
    and the speeds needs to be mentioned.

  3. you are right,if the speed of bee is 20 km/hr then distance traveled by it is 100 km.