Why do we take X runs nk+0.5 laps? Ok .5 is also understood, can you put some light on the 'nk' term.
virtualanimosity wrote:
Can any1 pls explain da concept behind such circular motion problem n meeting at startin pt problems
Q.Divi and Dave run on a circular track.Divi completes 3 laps in every 4 mins, and Dave completes 2 laps in every 3 mins in opposite direction.
Both start from points opposite to each other.Find the number of completed laps travelled by Divi when both will meet for the 3rd time at starting point of Dave.
1. 12
2. 13
3. 22
Let's call Divi X and Dave Y, would be much easier. They
start from the opposite points on the circular track. We need to find the
# of completed laps by X when they
meet 3rd time at the
starting point of Y.
Well first of all it's obvious that X will run number of complete laps and a half of the lap, as they are going to meet at the starting point of Y, which is half of the lap away from the starting point of X.
Speed of X - \(\frac{3}{4}\) L/M;
Speed of Y - \(\frac{2}{3}\) L/M;
Let's calculate when are they going to meet first time at the starting point of Y: Y will run some # of complete laps =n, and X will run k times laps plus 1/2 lap (as he starts at the opposite point)=\(nk+0.5\) \((k>0)\).
Time needed for this will be equal: \(\frac{n}{(2/3)}=\frac{(nk+0.5)}{3/4}\)--> \(n=\frac{8}{(18-16k)}\).
As \(n\) is integer value of the laps Y should run, the only possible value for k is 1, so n=4.
Which means that they will meet for the first time when Y will complete 4 laps and X 4.5 laps.
Ratio of the speed of Y to the speed of X=\((2/3)/(3/4)=\frac{8}{9}\). Which means that after their first meeting they will meet again and again at the same point each time when Y will complete 9 laps and X will complete 8. So, for the time of third meeting X will complete \(4.5+8+8=22.5\) or \(22\) full laps.
Answer: 3 (22).