$6$ A gravity dam $60$ m high, top width of $10$ m has a constant slope of $1$ vertical to $0\mathrm{.}5$ horizontal on upstream and of $0\mathrm{.}75$ horizontal to $1$ vertical on $\frac{d}{s}$ side. The water height corresponding to full reservoir level is $55$ m $.$ Calculate net vertical and net horizontal forces acting on dam profile. Also calculate factor of safety against sliding and overturning. Take unit weight of dam material as $24k\frac{N}{m^3},$ coefficient of uplift pressure as $0\mathrm{.}75.$