Problem $3(50$ points$)$

Given: A wave of $0\mathrm{.}75$ ft $.$ wave height and period $1\mathrm{.}6$ seconds is generated in a wave tank. The

wave tank is $150$ ft $.$ long, $8$ ft $.$ wide, and $15$ ft $.$ deep and filled with fresh water to a depth of $12$

ft$.$

Required:

a$)(30$ points$)$ Evaluate the length, wave celerity, and group celerity. Use US Units.

b$)(15$ points$)$ Determine the water particle velocity at a depth of $2$ ft $.$ below the still water

level $($SWL$)$ and $8\mathrm{.}3$ ft $.$ ahead of the wave crest. Use US Units. $($Hint: what is the phase

angle, of a wave $8\mathrm{.}3$ ft $.$ ahead of the wave crest? What is the $z$ value $2$ ft BELOW the

SWL$?)$

c$)(5$ points$)$ Draw the water particle velocity vector at this location and time.