Two persons (A and B) face to face apart from each other S (m) from nose to nose

Question

Two persons (A and B) face to face apart from each other S (m) from nose to nose walk towards each other on the same straight line. Person A moves with speed v (m/sec), and Person B also move with speed v (m/sec). A bee is in between the two persons flying from the nose of person A to the nose of person B and back and forth continuously with speed 2v (m/sec), twice the speed of the two persons. Assume that we do not consider the bee's mass and length, assume it's just a dot, a particle. What does the bee the total distance travel when the noses of the two persons crash, i.e., noses touch each other? How many times can the bee fly back and forth before the two persons crash? Can the bee fly infinite times before the two persons crash?

Explanation / Answer

1) time taken to meat the two persons, t = d/relative velocity

t = s/(2*v)

distance travelled by bee in this time, d = velocity*time taken

= 2*v*(s/(2*v))

= s

2) infinite times

3) yes.

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