Trenching to a depth of 48" for water lines

[jack stand]

Keep in mind that a chain dug 6"+/-" wide trench is much easier to restore to almost original than a backhoe dug trench.
My bigger is better suggestion was for definitely hitting your desired depth and having the backhoe as a backup and it'll be a benefit at each termination of the ditch against a building and the frost proof hydrant.
Just cleaning up after the outriggers of a regular backhoe will widen the "repair zone" wildly beyond what you'll have with a ditch which.

 

[Wamsutta]

That one you have pictured is for sprinkler lines. It's not going to go down 48 inches.

What you need is a mini excavator.

 

[dcg9381]

What you need is a mini excavator.

With a narrow bucket. It'll be slow work, but get you down to 48" no problem... Assuming you don't have "real rocks" to deal with. Often they have a blade on them so you can easily cover the trench back up.

Big rocks? Big money.

 

[Zewnten]

Not really in the hands of a skilled operator

This right here. OP asks for opinions people give them then he spits on them for disagreeing with his incorrect assumptions, the whole time not acknowledging where the actual limitations with his project are.