A boat in a lock with lock door A a water height of $4\mathrm{.}2$ m$.$ Lock door B a height of $6$ m$.$ The

width of the locks is $10$ m$.$ Lock A to B $($where the boat is moored$)60$ m long. The boat is $4$

m wide, $14$ m long, and lies $1\mathrm{.}5$ m deep in the water. How to do e$?$

a$)$ Determine the force and power required for the boat to sail at a speed of $10$ km$/$h and a

drag coefficient of $0\mathrm{.}6.$ Also say what things you neglect or assume or something.

b$)$ What is the Reynolds number at this speed? You can use the length of the boat as the

unit of length.

c$)$ Is this a good number for a shipping vessel? Why$/$why not? How can you further reduce

the hydrostatic resistance? Explain.

d$)$ If the lock gate in A is raised $50$ cm in the vertical direction. How long does it take before

the water level in the lock has dropped?

e$)$ If the boat drives backwards and collides with lock door B$,$ a hole of $0\mathrm{.}5$ m$2$ in area is

created at a height of $3$ m$.$ The door in lock A is closed vertically again but remains stuck at

a height of $10$ cm$.$ After a very long time, what is the water level in the lock?