Q. 52

Six particles situated at the corners of a regular hexagon of side a move at a constant speed u. Each particle maintains a direction towards the particle at the next corner. Calculate the time the particles will take to meet each other.

Answer :

A regular hexagon has a side= a.


Six particles situated at the corners of the hexagon are moving with a constant speed v.


As per the question, each particle maintains a direction towards the particle at the next corner.


So, particles will meet at centroid O of triangle PQR.


Now, at any instant, the particles will form an equilateral triangle PQR with the same centroid O.
We know that P approaches Q, Q approaches R and so on.


Now, we will consider the motion of particle P. Its velocity makes an angle of.
This component is the rate of decrease of distance PO.


Relative velocity between P and Q:
Capture.PNG





Hence, the time taken by the particles to meet each other is


.


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Irodov Special Classes (Strengthen your concepts)Irodov Special Classes (Strengthen your concepts)Irodov Special Classes (Strengthen your concepts)45 mins
Motion in 1 DMotion in 1 DMotion in 1 D38 mins
Kinematics HCV Objective | Interactive QuizKinematics HCV Objective | Interactive QuizKinematics HCV Objective | Interactive Quiz71 mins
Interactive Quiz on Relative velocity (Rain Problem)Interactive Quiz on Relative velocity (Rain Problem)Interactive Quiz on Relative velocity (Rain Problem)32 mins
Relative velocity (River Problem)Relative velocity (River Problem)Relative velocity (River Problem)42 mins
Goprep Genius Quiz | Full Kinematic TestGoprep Genius Quiz | Full Kinematic TestGoprep Genius Quiz | Full Kinematic Test43 mins
Complete Revision in an Hour | KinematicsComplete Revision in an Hour | KinematicsComplete Revision in an Hour | Kinematics57 mins
Goprep Genius | Kinematics TestGoprep Genius | Kinematics TestGoprep Genius | Kinematics Test40 mins
Equations Of Motion from Calculus MethodEquations Of Motion from Calculus MethodEquations Of Motion from Calculus Method46 mins
Feel Confident About Solving Projectile Motion ProblemsFeel Confident About Solving Projectile Motion ProblemsFeel Confident About Solving Projectile Motion Problems35 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses