Question

Two particles are originally placed at P and Q distant d apart. At zero instant, they start moving such that velocity $\overrightarrow{v}$ of P is aimed towards Q and velocity $\overrightarrow{u}$ of Q is perpendicular to $\overrightarrow{v}$. The two projectiles meet at time T =

• A. $\frac{\left( v^{2} - u^{2} \right)d^{2}}{v^{3}d}$
• B. $\frac{(v + u)d}{v^{2}}$
• C. $\frac{v(v - u)}{d}$
• D. $\frac{vd}{\left( v^{2} - u^{2} \right)}$

Answer 1

Answer: (D)

$\frac{vd}{\left( v^{2} - u^{2} \right)}$

Answer 2

Relative velocity of P and Q is (v – u cos θ). The particles will meet when

$\int_{0}^{Τ}{\left( v - u\cos\theta \right)dt}$ = d and $\int_{0}^{Τ}{v\cos\theta dt}$ = d

and $\int_{0}^{Τ}{\cos\theta dt} = \frac{uT}{v}$ or vT – u $\frac{uT}{v}$ = d or (v² – u²)T= vd

or T = $\frac{vd}{v^{2} - u^{2}}$