(Solved): As shown, a pipe is anchored to a wall at point A. (Figure 2) During the pipe's installation, severa ...

Learning Goal: To understand the concept of moment of a force and how to calculate it using a scalar formulation. The magnitude of the moment of a force with a magnitude $F$ around a point $O$ is defined as follows: $M_O=Fd$ where $d$ is the force's moment arm. The moment arm is the perpendicular distance from the axis at point $O$ to the force's line of action. A stool at a restaurant is anchored to the floor. When a customer is in the process of sitting down, a horizontal force with magnitude $F_1$ is exerted at the top of the stool support as shown in the figure. (Figure 1) When the customer is seated, a vertical force with magnitude $F_2$ is exerted on the stool support. If the maximum moment magnitude that the stool support can sustain about point $A$ is $M_A=250\mathrm{N}?\mathrm{m}$, what is the maximum height $d_1$ that the stool can have if the magnitudes of the two forces are $F_1=130\mathrm{N}$ and $F_2=840\mathrm{N}$ ? Assume that moments acting counterclockwise about point $A$ are positive whereas moments acting clockwise about $A$ are negative. Express your answer numerically in meters to three significant figures.