Answer
See answers.
Work Step by Step
It is best to use $\Sigma p_i=\Sigma p_f$ when the system consists of multiple objects and we may ignore external forces, i.e., only the forces between objects are significant.
The principle of impulse is useful for a single object, when the average external force is known, or the time over which the force acts is known, and we are considering the object’s change in momentum.
