The story is about the increased rainfall causing the lake in Abidij Park to overflow. Image of the lake given. The lake can be assumed to be rectangular with dimensions of $400\backslash$times $200$ m$.$ The water level given was $1$ m$.$ The dam wall was triangular with a base of $0\mathrm{.}5$ m and height of $1\mathrm{.}5$ m$.$

a$)$ Determine the vertical and horizontal force on the dam wall.

b$)$ The rainfall was recorded to be $30$ litres per square meter every hour. What was the increase of water level in the lake in one hour.

c$)$ The dam breaks and water starts flowing to the lower lying areas, including Professor Vanierschot's garden. Suddenly, he sees a ball floating in the water with a depth of $8$ cm$.$ The volume of a sphere hat is given as $1/3*$pi$*$h$^2(3$R $-$ h$).$ What is the weight of the ball?

d$)$ Water starts flowing into his house through a small slit at the bottom of the door of $0\mathrm{.}5$ mm$.$ The door itself has a width of $86$ cm$.$ Determine the flow$-$rate of water into the house.

e$)$ How long does it take for the water level in the house to reach $2$ cm$?$ The house has an area of $80$ m$^2$ and you can assume that there is no water flowing out.