$1.$ A rectangular channel is $10$ ft wide and carries a discharge of $300$ cfs $.$ The Manning's roughness coefficient is $0\mathrm{.}025.$ There is a gate in the middle of the channel and its opening is $1\mathrm{.}8$ ft $.$ Determine if a hydraulic jump occlur after the gate in the following two cases. Show your calculations which are used to make your judgement if hydraulic jump occurs or not.

a$)$ If the bottom slope of the channel is $0\mathrm{.}02$

b$)$ If the bottom slope of the channel is $0\mathrm{.}002$