Final answer:
Cations enter root hairs through active transport, where proteins use ATP to move these ions against the concentration gradient from lower to higher concentration areas.
Step-by-step explanation:
The cations enter root hairs predominantly through a process known as active transport. During active transport, proteins in the cell membrane use energy, typically in the form of ATP (adenosine triphosphate), to move cations from an area of lower concentration to an area of higher concentration, effectively going against the concentration gradient. This is crucial for the absorption of nutrients by plants as they often need to absorb ions from the soil where they might be at a lower concentration than inside the root hair cells.
Unlike diffusion or osmosis, which are examples of passive transport and occur along the concentration gradient, active transport requires energy input. Active transport is noted for being able to move substances across membranes regardless of the concentration gradient, making it essential for root hair cells to uptake essential cations.