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Three particles are located at the vertices of an equilateral triangle of side L. Each of the particle starts to move with constant speed v, with the first particle heading continuously for second, the second for the third, and the third for the first. When will the particle meet each other?
Most Upvoted Answer
Three particles are located at the vertices of an equilateral triangle...
**Solution:**
To solve this problem, we can consider the motion of each particle separately and find the time at which they meet each other.
Let's assume that the first particle starts at the origin (0, 0) and moves in the positive x-direction with constant speed v. The second particle starts at the vertex (L, 0) and moves towards the first particle. The third particle starts at the vertex (L/2, L√3/2) and moves towards the second particle.
**Determining the motion of the first particle:**
The first particle moves with constant speed v in the positive x-direction. We can describe its motion using the equation:
x1 = vt
where x1 is the x-coordinate of the first particle at time t.
**Determining the motion of the second particle:**
The second particle starts at the vertex (L, 0) and moves towards the first particle. The direction of its motion can be described by the unit vector u12 pointing from the second particle to the first particle:
u12 = (x1 - x2)/r12
where r12 is the distance between the second and first particles.
The motion of the second particle can be described by the equation:
x2 = (x1 - x2)/r12 * vt + L
Simplifying the equation, we get:
x2 = (x1 * vt + L * r12)/(r12 + 1)
**Determining the motion of the third particle:**
The third particle starts at the vertex (L/2, L√3/2) and moves towards the second particle. The direction of its motion can be described by the unit vector u23 pointing from the third particle to the second particle:
u23 = (x2 - x3)/r23
where r23 is the distance between the third and second particles.
The motion of the third particle can be described by the equation:
x3 = (x2 - x3)/r23 * vt + L/2
Simplifying the equation, we get:
x3 = (x2 * vt + L/2 * r23)/(r23 + 1)
**Determining the time at which the particles meet:**
To find the time at which the particles meet, we need to find the common value of x1, x2, and x3.
Substituting the equations for x1, x2, and x3 into each other, we can solve for t. The resulting equation will give us the time at which the particles meet.
Since the equations are quite complicated, it is recommended to use numerical methods or computer simulations to solve them and find the values of t at which the particles meet.
Overall, the particles will meet each other at a certain time t, which can be found by solving the equations for their motion.
To solve this problem, we can consider the motion of each particle separately and find the time at which they meet each other.
Let's assume that the first particle starts at the origin (0, 0) and moves in the positive x-direction with constant speed v. The second particle starts at the vertex (L, 0) and moves towards the first particle. The third particle starts at the vertex (L/2, L√3/2) and moves towards the second particle.
**Determining the motion of the first particle:**
The first particle moves with constant speed v in the positive x-direction. We can describe its motion using the equation:
x1 = vt
where x1 is the x-coordinate of the first particle at time t.
**Determining the motion of the second particle:**
The second particle starts at the vertex (L, 0) and moves towards the first particle. The direction of its motion can be described by the unit vector u12 pointing from the second particle to the first particle:
u12 = (x1 - x2)/r12
where r12 is the distance between the second and first particles.
The motion of the second particle can be described by the equation:
x2 = (x1 - x2)/r12 * vt + L
Simplifying the equation, we get:
x2 = (x1 * vt + L * r12)/(r12 + 1)
**Determining the motion of the third particle:**
The third particle starts at the vertex (L/2, L√3/2) and moves towards the second particle. The direction of its motion can be described by the unit vector u23 pointing from the third particle to the second particle:
u23 = (x2 - x3)/r23
where r23 is the distance between the third and second particles.
The motion of the third particle can be described by the equation:
x3 = (x2 - x3)/r23 * vt + L/2
Simplifying the equation, we get:
x3 = (x2 * vt + L/2 * r23)/(r23 + 1)
**Determining the time at which the particles meet:**
To find the time at which the particles meet, we need to find the common value of x1, x2, and x3.
Substituting the equations for x1, x2, and x3 into each other, we can solve for t. The resulting equation will give us the time at which the particles meet.
Since the equations are quite complicated, it is recommended to use numerical methods or computer simulations to solve them and find the values of t at which the particles meet.
Overall, the particles will meet each other at a certain time t, which can be found by solving the equations for their motion.
Community Answer
Three particles are located at the vertices of an equilateral triangle...
2L/v×sqrt3 itte sec me centroid pr milega
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Three particles are located at the vertices of an equilateral triangle of side L. Each of the particle starts to move with constant speed v, with the first particle heading continuously for second, the second for the third, and the third for the first. When will the particle meet each other?
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Three particles are located at the vertices of an equilateral triangle of side L. Each of the particle starts to move with constant speed v, with the first particle heading continuously for second, the second for the third, and the third for the first. When will the particle meet each other? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Three particles are located at the vertices of an equilateral triangle of side L. Each of the particle starts to move with constant speed v, with the first particle heading continuously for second, the second for the third, and the third for the first. When will the particle meet each other? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Three particles are located at the vertices of an equilateral triangle of side L. Each of the particle starts to move with constant speed v, with the first particle heading continuously for second, the second for the third, and the third for the first. When will the particle meet each other?.
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