Two particles start simultaneously from the same point and move along two straight lines

• Differentiation

Two particles start simultaneously from the same point and move along two straight lines, one with uniform velocity u and the other from rest with uniform acceleration f. Let α be the angle between their directions of motion. The relative velocity of the second particle w.r.t. the first is least after a time

1. t = (u sin α)/f
2. t = (f cos α)/u
3. t = (u sin α)
4. t = (u cos α)/f

Answer

After time t,

Velocity = f × t

V_BA = (f × t) + (−u) =

V_BA² = (f² t² + u² - 2fut cos α)

For max and min

d/dt(V_BA²) = 0

2f² t - 2fu cos α = 0

t = (u cos α)/f

The correct option is D.