Three particles A,B and C are situated at the vertices of an equilateral triangle ABC of side a at=0. Each of the particles moves with a constant speed v. A always has its velocity along AB , B along BC and C along CA . At what time will these particles meet each other?
I dont understand this question because it seems that the particles are restricted to the sides of the triangle, and are always moving away from each other.
There is a solution here, but I don't understand it. https://doubtnut.com/question-answer-physics/three-particles-a-b-and-c-are-situated-at-the-vetices-of-and-equilateral-triangle-abc-of-side-a-at-t-11762860
Physics rectilinear motion question 3 particles, stumped. Please help.?
2020-10-10 12:58 am
回答 (2)
2020-10-10 11:10 am
The particles are all moving toward the center of the triangle, and are moving along curved paths as they do so. (They are not moving away from each other.)
What the referenced solution does is determine the speed with which the particles approach each other. (That makes the specific path irrelevant.) Due to the geometry of an equilateral triangle, the approach speed is
V = v + v*cos60º = v + v/2 = 3v/2
Since they were initially "a" apart, the time is
t = a / V = a / 3v/2 = 2a / 3v
What the referenced solution does is determine the speed with which the particles approach each other. (That makes the specific path irrelevant.) Due to the geometry of an equilateral triangle, the approach speed is
V = v + v*cos60º = v + v/2 = 3v/2
Since they were initially "a" apart, the time is
t = a / V = a / 3v/2 = 2a / 3v
參考: image from stackexchange.com
2020-10-10 3:48 am
The particles make up the triangle.
When the particles move, the triangle moves.
"A always has its velocity along AB"
A and B are particles. So this means that A is always going in the direction of B. B is always going in the direction of C... The triangle gets smaller and rotates until they all finally collide at the center.
When the particles move, the triangle moves.
"A always has its velocity along AB"
A and B are particles. So this means that A is always going in the direction of B. B is always going in the direction of C... The triangle gets smaller and rotates until they all finally collide at the center.
收錄日期: 2021-04-24 08:05:17
原文連結 [永久失效]:
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