Final answer:
In straight-and-level flight, the lift force on a plane must equal and oppose the weight force. During a banked turn, the horizontal component of lift allows the plane to accelerate in the direction of the turn. The vertical component of lift counters the weight of the plane, maintaining its altitude.
Step-by-step explanation:
In straight-and-level unaccelerated flight, the lift and weight vector must be equal and opposite in order for the plane to maintain its altitude. The lift force, generated by the air acting on the wing, counteracts the weight of the plane. The lift force has both vertical and horizontal components.
When the plane is banking to make a turn, the lift force is tilted, causing a horizontal component of lift that accelerates the plane in the direction of the turn. This imbalance of forces allows the plane to change direction while maintaining altitude.
It's important to note that in unaccelerated flight, the vertical component of lift exactly balances the weight of the plane, while the horizontal component of lift allows for changes in velocity and direction.