What you are looking for is a sort of velocity match between the two objects. You can obtain it by checking the target (first projectile) velocity and modifying the second one according to this.
The pseudo code is something like:
max_acceleration. First and second values are the current velocities of projectiles and other twos are used to tweak the behavior of the chase. Of course you should use vectors (but I suppose you do, since it's the only way to manage these things).
Then at every update:
result_acceleration = target_velocity - this_velocity;
result_acceleration /= time_to_match;
if (result_acceleration.magnitude() > max_acceleration)
result_acceleration *= max_acceleration;
result_acceleration value is applied as usually within a physics engine to current
this_velocity of following projectile. In your case the
time_to_match variable should be enough small to keep the two objects tights (eg. 0.05-0.1).