Two runners start simultaneously from the same point on a
circular 200-m track and run in same directions. One runs at a
constant speed of 6.20 m/s, and the other runs at a constant speed
of 5.50 m/s.
when will the fast one overtake the slower one?
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this may be an easy problem, but I am getting confused... as far as I have analyzed.. the distance traveled for overtaking is same and the time taken for overtaking is different....
If this is the correct analysis.. then I am not able to proceed further... can yiu help me to proceed??
Thanxx..!!!
The faster one is going to travel more distance. Time is going to be the same.
Method I
Let us say the faster one completes n full revolutions + x distance and the slower one completes m full revolutions + x distance. Then, we have:
\(\frac {2\pi r.n+x}{6.20}=\frac {2\pi r.m+x}{5.50}\)
Where n and m are the number of turns which should be minimum for x < 200. x is the extra distance after full revolutions.
Method II
Let the slower one be the reference frame. The faster one will take a few additional full revolutions with respect to the slower one.
\(0.7=\frac {2\pi r.n}{t}\)
n is the smallest natural number.