 17
 0
1. Homework Statement
Three ants A, B and C are crawling on a large horizontal tabletop always occupying vertices of an equilateral triangle, size of which may vary with time. If at an instant, speeds of A and B are vA and vB, prove that vC>= vA+vB.
2. Homework Equations
Well, that's what I don't understand to always maintain the shape of an equilateral triangle, one of the paths they may acquire is constantly approach each other.
3. The Attempt at a Solution
First I considered them to move along the equilateral triangle but using cosine law doesn't help. If they approach each other, I got the relation that their velocities must be equal since:
We write the
for A approaching B as
. Now, all the velocity of approaches must be equal in order to form an equilateral triangle at every point. So
are all equal, which means that
This gives that
.
What to do now in order to make a solid conclusion?
Three ants A, B and C are crawling on a large horizontal tabletop always occupying vertices of an equilateral triangle, size of which may vary with time. If at an instant, speeds of A and B are vA and vB, prove that vC>= vA+vB.
2. Homework Equations
Well, that's what I don't understand to always maintain the shape of an equilateral triangle, one of the paths they may acquire is constantly approach each other.
3. The Attempt at a Solution
First I considered them to move along the equilateral triangle but using cosine law doesn't help. If they approach each other, I got the relation that their velocities must be equal since:
We write the
What to do now in order to make a solid conclusion?
Attachments

1.2 KB Views: 416

4 KB Views: 400

1.2 KB Views: 454

1.7 KB Views: 454

1.5 KB Views: 414