Q. Three particles A B & C start from the origin at the same time; A with U velocity 'a' along x - axis, B with a velocity 'b' along y-axis and C with velocity 'c' in XY plane along the line x = y. The magnitude of 'c' so that the three always remain collinear is :
Motion in a Plane
Solution:
comparing the slopes $\frac{b - \frac{c}{\sqrt{2}}}{0 - \frac{c}{\sqrt{2}}} = \frac{b - 0}{0 - a}$
$\frac{b - \frac{c}{\sqrt{2}}}{ \frac{c}{\sqrt{2}}} = \frac{b }{a} = ab - \frac{ac}{\sqrt{2}} = \frac{bc}{\sqrt{2}}$
$\therefore \, ab = \frac{c (a + b)}{\sqrt{2}}$
$c = \frac{\sqrt{2} ab}{a + b}$
