Answer
$x=0.7m$
Work Step by Step
Let's choose the axis of rotation to be at the support on the right.
- The plank's weight $W_1=225N$ produces a counterclockwise (positive) torque. Because the plank is uniform, center of gravity is at the midpoint $2.5m$ from each end, so the lever arm is $2.5-1.1=1.4m$
- The person's weight $W_2=450N$ produces a clockwise (negative) torque. The lever arm is $x$
Because the system is in equilibrium, $$\sum\tau=1.4W_1-xW_2=0$$ $$x=\frac{1.4W_1}{W_2}=0.7m$$
