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3-2.Motion in Plane
normal
Two particles, one at the centre of a circle of radius $R$, and another at a point $Q$ on the circle, start moving towards a point $P$ on the circle at the same time (see figure below). Both are at rest initially and move with uniform velocities $\vec{V}_1$ and $\overrightarrow{V_2}$ respectively. They also reach the point $P$ at the same time, If the angle between the velocities is $\theta$ and the angle subtended by $P$ and $Q$ at the centre is $\phi$ (as shown in the figure), then
A$\tan \frac{\phi}{2}=\cot \theta$
B$\tan \phi=\cot \theta$
C$\cot \frac{\phi}{2}=\cot \theta$
D$\tan \frac{\phi}{2}=\cot \frac{\theta}{2}$
(KVPY-2021)
Solution
(A)$\frac{\phi}{2}+\theta=90^{\circ}$
$\frac{\phi}{2}=90-\theta$
$\tan \frac{\phi}{2}=\tan (90-\theta)=\cot \theta$
$\tan \left(\frac{\phi}{2}\right)=\cot \theta$
Standard 11
Physics
