Question

Two particles are projected simultaneously from two points, O and O' such that d is the horizontal distance and h is the vertical distance between them. They are projected at the same inclination a to the horizontal with the same speed v. The time after which their separation becomes minimum is-

• A. d(v cosa)
• B. 2d/(v cosa)
• C. d/(2v cosa)
• D. d/v

Answer 1

Answer: (C)

d/(2v cosa)

Answer 2

As the vertical component of velocity of both the particles is same.

̃ $\overrightarrow { \mathrm { V } } _ { \mathrm { yO } / \mathrm { O } ^ { \prime } }$ = 0

So the distance h between them will be constant with time and $\overrightarrow { \mathrm { v } } _ { \mathrm { xO } / \mathrm { O } ^ { \prime } }$ = 2v cos a

Total distance between the particles is minimum when horizontal distance between them is zero.

̃ t = $\frac { \mathrm { d } } { 2 \mathrm { v } \cos \alpha }$