(Solved): Q1 The rectangular gate shown below in figure Q1 has dimension \( 3 \mathrm{~m} \) long and \( 2 \m ...

Q1 The rectangular gate shown below in figure Q1 has dimension \( 3 \mathrm{~m} \) long and \( 2 \mathrm{~m} \) wide. It is pin connected at Point \( \mathrm{A} \). The surface that the gate rests on at Point \( \mathrm{B} \) is frictionless. Find that following (i) The depth to the geometric centre, \( \bar{y} \) (10 Marks) (ii) The Resultant Force, \( R \) (20 Marks) (iii) The depth, \( D \) at which the Resultant Force acts (30 Marks) (iv) The reaction force at point B at this depth when the Gate is closed (40 Marks)