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 :
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 :
Updated On: Nov 13, 2023
- $\frac{a+y}{2}$
- $\sqrt{ab}$
- $\frac{ab}{a+b}$
- $\frac{\sqrt{2}ab}{a+b}$
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The Correct Option is D
Solution and Explanation
comparing the slopes $\frac{b - \frac{c}{\sqrt{2}}}{0 - \frac{c}{\sqrt{2}}} = \frac{b - 0}{0 - a}$
$\frac{b - \frac{c}{\sqrt{2}}}{ \frac{c}{\sqrt{2}}} = \frac{b }{a} = ab - \frac{ac}{\sqrt{2}} = \frac{bc}{\sqrt{2}}$
$\therefore \, ab = \frac{c (a + b)}{\sqrt{2}}$
$c = \frac{\sqrt{2} ab}{a + b}$
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Notes on Motion in a plane
Concepts Used:
Motion in a Plane
It is a vector quantity. A vector quantity is a quantity having both magnitude and direction. Speed is a scalar quantity and it is a quantity having a magnitude only. Motion in a plane is also known as motion in two dimensions.
Equations of Plane Motion
The equations of motion in a straight line are:
v=u+at
s=ut+½ at2
v2-u2=2as
Where,
- v = final velocity of the particle
- u = initial velocity of the particle
- s = displacement of the particle
- a = acceleration of the particle
- t = the time interval in which the particle is in consideration