which of the following is the best management tool to determine the longest time the project will take?(WBS-Bar chart -Network diagram-Project charter

Network diagram is the tool helpful to identify the longest time project takes. There are many methods, but most familiar is Critical path method.

Detailed activities from WBS must be included in ND with time duration to identify Critical paths/longest durations.

Critical Path Method Chart, otherwise known as Network Diagram.

Network Diagram using critical path method.

Network diagram

Network Diagram

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Network diagram

Network diagram

Network diagram

Network Diagram using CPM

Typically, WBS doesn't contain duration.
Project Charter can only give you limitations, not the real time it should take.
On the other hand, Bar chart and network diagram are two effective tools to represent timing: Bar chart can be effective to see how activities/ tasks are flowing, network diagrams can give the relations and interdependencies, but both cant work separately.
Actually, to control timing, you need to make a blend of them both in a way you can see the flow and durations with the relations visible.
For projects with huge numbers of activities you cant do it manually and you cant see all activities or relations at the same time, so you will need a software that have both Network diagrams and Bar charts like Primavera, Ms project,...etc.