Question

The particles are separated at a horizontal distance $x$ as shown in the figure. They are projected at the same time as shown in the figure with different initial speeds. The time after which the horizontal distance between the particles become zero is

• A. $\frac{u}{2x}$
• B. $\frac{x}{u}$
• C. $\frac{2u}{x}$
• D. $\frac{u}{x}$

Answer 1

The correct option is B $\frac{x}{u}$

Let $x_1$ and $x_2$ are the horizontal distance travelled by particle $A$ and $B$ repectively in time $t$
So, $x_1=\frac{u}{\sqrt{3}}.\cos {30}^{\circ }\times t=\frac{ut}{2}$........(i)
And, $x_2=u.\cos {60}^{\circ }\times t=\frac{ut}{2}$.........(ii)
$\therefore$ On (i)+(ii) we have,
$x_1+x_2=ut$
Or, $x=ut⟹t=\frac{x}{u}$