Question

Three persons P, Q and R of same mass travel with same speed u along an equilateral triangle of side 'd' such that each one faces the other always. After how much time will they meet each other.

• A. $\frac{d}{u}$ seconds
• B. $\frac{2d}{3u}$ seconds
• C. $\frac{2d}{\sqrt{3}u}$ seconds
• D. $\frac{d}{\sqrt{3}u}$ seconds

Answer 1

The correct option is B $\frac{2d}{3u}$ seconds

$QC=\frac{2}{3}\sqrt{a^2-{\left(\frac{d}{2}\right)}^2}=\frac{d}{\sqrt{3}}$

so time taken for QC becomes zero

$=\frac{\frac{d}{\sqrt{3}}}{u\cos {30}^{\circ }}$

$=\frac{\frac{d}{\sqrt{3}}}{u\times \frac{\sqrt{3}}{2}}$

$=\frac{2d}{3u}seconds$