English, asked by rahulcolasso, 1 year ago

Twelve persons are initially at twelve corners of a regular polygon of twelve side of side length a. Each person
now moves with uniform speed V in such a manner that he is always directed towards the adjacent person in
sequence and so on. The distance travelled by each person before they meet is .

Answers

Answered by shailendrachoubay216
5

The distance travelled by each person before they meet is 7.464×a.

Explanation:

1. Here are 12 person on vertices of regular polygon. For regular hexagon each exterior angle is 30 degree.

2. So change in direction of each person velocity is by 30 degree.

3. On taking First two person.

   Velocity of first person V_{1}= V

   Velocity of second person  V_{2}= V\cos 30^{\circ}

4. velocity of second person with respect to second person

    V_{21}= V\cos 30^{\circ} - V =-V(1 -\cos 30^{\circ} )\\  ...a)

   negative sign indicate that distance between first and second person is decreasing.

5. On taking absolute speed of second person with respect to second person

 V_{21}= V(1 -\cos 30^{\circ} )         ...b)

6. Time taken by person second to cover distance (a) speed V_{21}.

 Time (t) = \frac{distance}{speed} = \frac{a}{V(1 -\cos 30^{\circ} )}  ...c)

7. Now distance cover by any person with speed V in time(t) from equation-c)

Distance travelled by each person before they meet = Speed×Time

Distance travelled by each person before they meet = V\times \frac{a}{V(1 -\cos 30^{\circ} )}= 7.464a

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