Two bodies of equal mass are at rest, side by side. A constant force F is applied on the first body while at the same instant an impulsive force, producing an impulse I is applied in the same direction on the second body. Determine the time taken by them, in terms of F and I, to be side by side again.

Explanation

Let the mass of each body be m, and the times when they are side by 0 and t s.
Acceleration of the first body due to F, a = `(F)/(m)`.
`therefore` Displacement of the first body in time t, starting from rest,
`s_(1) = (1)/(2)cdot (F)/(m)cdot t^(2) = (Ft^(2))/(2m)`
The change in momentum of the second body due to impulse,
I = change in momentum
= mv - mu = mv - m `xx` 0 = mv
or, `v = (I)/(m)`
As no other force acts on the second body, it moves with this constant velocity (v) for t s, and covers a distance `s_(2)`.
`therefore " " s_(2) = vt = (I t)/(m)`
According to the problem `s_(1) = s_(2)`
`therefore " "(Fr^(2))/(2m) = (I t)/(m) ` [ from (1) and (2) ]
`therefore " " t = (2I)/(F)` .