Question

three particles A,B and C start from origin at same time A with velocity a along x- axis ,B with velocity b along y axis and C with velocity c in X-Y plane along line x=y.the magnitude of c so that three are always collinear is?

Answer 1

Answer on Question #63660-Physics-Mechanics-Relativity

Three particles A, B and C start from origin at same time A with velocity a along x-axis, B with velocity b along y axis and C with velocity c in X-Y plane along line x=y. the magnitude of c so that three are always collinear is?

Solution

c is the bisector of triangle:

$$c = \frac {\sqrt {a b ((a + b) ^ {2} - (a ^ {2} + b ^ {2}))}}{a + b} = \frac {\sqrt {a b ((a ^ {2} + b ^ {2} + 2 a b) - (a ^ {2} + b ^ {2}))}}{a + b} = \frac {\sqrt {a b (2 a b)}}{a + b} = \frac {\sqrt {2} a b}{a + b}.$$

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