Question

A carpenter is using $8\text{d}$ (8-penny) common nails to fasten a subfloor board with an actual thickness of $1.0\text{ inch}$ to underlying framing joists. For standard nails between $2\text{d}$ and $10\text{d}$, the total nail length $L$ in inches is determined by the formula $L = \frac{d}{4} + 0.5$, where $d$ is the penny size. Assuming the nail is driven perpendicular and flush with the top surface of the subfloor, what is the depth of penetration (in inches) of the nail into the framing joist?