I need help solving this exercise step by step, please.

$[7-2]$ Terzaghi discussed the failure state shown in Fig. $7\mathrm{.}2$ below as a failure problem of soil just below the foundation with no friction between the lower surface of the foundation and the soil ground $($unit weight $=,$ cohesion $=c$ and angle of internal friction $=).$ This failure region is divided into three zones: zone I: wedge shape part immediately beneath the footing $($foundation$),$ zone III: wedge shape part where the side of the footing suffers passive failure, and zone II: this area lies between zone I and zone III. The failure region for zone II is represented using a logarithmic spiral. Let the surface of the soil wedge immediately beneath the footing make an angle with the horizontal which is equal to the internal friction angle, $.$ Also, in the case where the foundation is buried within the ground at depth $D_f,$ then the effective overburden pressure is replaced by the surcharge load, $q_s=D_f,$ where $D_f$ is the depth of the footing from the ground surface and $$ is the unit weight of soil. Neglecting the self$-$weight of the soil, find the bearing capacity formula for sandy ground $(c=0)$ by following the steps below.

$(1)$ By dividing the failure region into zone I, zone II and zone III, find and show the forces that act in each zone. $P_1,P_2$ and $R$ are the forces that act on surfaces $OA,OB$ and AB shown in the figure.

$(2)$ Show the equilibrium of forces that act on zone I and zone III. For zone III, $\frac{?}{\text{b}\text{a}\text{r}}(BC)=H.$ Calculate the passive earth pressure for this zone.

$(3)$ If the shape of the transient region $($zone II$)$ is represented by $r_2=r_1$exp$(tan),$ then by taking the equilibrium of moments around the point O $,$ find the relationship between $P_1$ and $P_2,r_2\frac{?}{b}=ar(OA),r_2\frac{?}{b}=ar(OB)$ and $\frac{?}{{?}_A}=OB.$

$(4)$ Find the relationship between the foundation width, $B$ and $H.$

$(5)$ From the results of $(1),(2),(3)$ and $(4),$ solve the bearing capacity equation for sand,

$\frac{Q}{B}=q_s{N}_q$

$($Substitute the values of $P_1,P_2,r_1,r_2,$ and $H.)$ By considering $c0$ and the weight of soil mass, it is possible to find a bearing capacity equation for general soil following the steps mentioned above, but the bearing capacity factors $N_c$ and $N_{}$ become functions of internal friction angle, $$ as that of $N_q$ obtained in $(5).$