Question $5$: Curved Surface

The gate $AB$ shown below is hinged at A and rests against a perfectly smooth vertical wall. The width of the gate is $5m$ long with water as shown. Find the following:

a$)$ The horizontal component $(P_H)$ of the Total Hydrostatic Pressure

b$)$ The vertical component $(Pv)$ of the Total Hydrostatic Pressure

c$)$ The Total Hydrostatic Pressure P

d$)$ The angle of inclination $$ from the horizontal axis. Use density of water $=1,000k\frac{g}{m^3}.$

e$)$ The distance $\text{'}y\text{'}$ of $P_H$ from point $B$

f$)$ The distance $\text{'}x\text{'}$ of $P_V$ from point $B$