Question

Time when their velocities will become perpendicular is

• A. 1 sec
• B. 2 sec
• C. 3 sec
• D. none of these

Answer 1

Answer: (B)

2 sec

Velocities of the particles at any time $t$
${\overrightarrow{V}}_1=u_1\hat{i}-gsin\theta t\hat{j}$
${\overrightarrow{V}}_2=-u_2\hat{i}+-gsin\theta t\hat{j}$
time when their velocities will be perpendicular will be
${\overrightarrow{V}}_1.{\overrightarrow{V}}_2=0\Rightarrow 0=-u_1{u}_2+g^{2}si{n}^2\theta t^2$
$\Rightarrow t=\frac{\sqrt{u_1{u}_2}}{gsin\theta }=\frac{\sqrt{20\times 5}}{10\times \left(\frac{1}{2}\right)}=2sec.$