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 :

Question

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 : (A) (a+y/2) (B) √ab (C) (ab/a+b) (D) (√2ab/a+b)

Tardigrade Admin · Accepted Answer

comparing the slopes (b - (c/√2)/0 - (c)√2) = (b - 0/0 - a) (b - (c/√2)/ (c)√2) = (b /a) = ab - (ac/√2) = (bc/√2) ∴ ab = (c (a + b)/√2) c = (√2 ab/a + b)

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 :

$\frac{a + y}{2}$

$ab$

$\frac{ab}{a + b}$

$\frac{2 ab}{a + b}$

comparing the slopes $\frac{b - \frac{c}{2}}{0 - \frac{c}{2}} = \frac{b - 0}{0 - a}$
$\frac{b - \frac{c}{2}}{\frac{c}{2}} = \frac{b}{a} = ab - \frac{a c}{2} = \frac{b c}{2}$
$∴ ab = \frac{c ( a + b )}{2}$
$c = \frac{2 ab}{a + b}$

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 :

2a+y​

ab​

a+bab​

a+b2​ab​

comparing the slopes 0−2​c​b−2​c​​=0−ab−0​ 2​c​b−2​c​​=ab​=ab−2​ac​=2​bc​ ∴ab=2​c(a+b)​ c=a+b2​ab​

$\frac{a + y}{2}$

$ab$

$\frac{ab}{a + b}$

$\frac{2 ab}{a + b}$

comparing the slopes $\frac{b - \frac{c}{2}}{0 - \frac{c}{2}} = \frac{b - 0}{0 - a}$
$\frac{b - \frac{c}{2}}{\frac{c}{2}} = \frac{b}{a} = ab - \frac{a c}{2} = \frac{b c}{2}$
$∴ ab = \frac{c ( a + b )}{2}$
$c = \frac{2 ab}{a + b}$