Consider a person doing push$-$ups viewed from the side. Assume that the body is straight with the legs, torso, neck, and head perfectly aligned. The arms are bent at the elbows such that the body is perfectly horizontal, the hands are directly above the shoulders, the hands are flat on the ground, and the feet are perpendicular to the legs. The lengths of each body part measured from joint to joint are as follows:

Feet $20cm$

Legs from ankles to hips $90cm$

Torso from hips to shoulders $50cm$

Neck and head from shoulders to top of head $40cm$

Arms from shoulder to elbow $25cm$

Forearms from elbow to hand $25cm$

The mass per unit length of each body part is as follows $($neglect the mass $$ feet and arms$)$:

Legs $40k\frac{g}{m}$

Torso $50k\frac{g}{m}$

Neck and head $20k\frac{g}{m}$

Consider that mass is uniformly distributed along the length of each body part.

$(1)$ The body $($including feet and arms$)$ is assumed to be a rigid object and it is the structure of interest. Draw a $2$D free body diagram of the entire body and calculate the reaction forces and moments at the hands and toes.

$(2)$ Now, consider that the structure of interest excludes the arms. Draw a free body diagram of the structure of interest and calculate the forces and moment at the shoulders.

$(3)$ Now assume that the hands are placed $15cm$ forward $($i$.$e$.,$ at the level of the head$).$ Calculate the new supports at the shoulders.