Final answer:
During takeoff, an aircraft's engine thrust provides vertical force to counteract gravity and horizontal force to accelerate forward, while banking maneuvers use the lift force for turns.
Step-by-step explanation:
The thrust of an aircraft's engine during takeoff provides both vertical and horizontal forces due to the principles of physics that govern flight.
The vertical component of thrust counteracts the weight of the aircraft, allowing it to rise off the ground, while the horizontal component accelerates it forward along the runway to achieve the necessary speed for lift-off.
By banking, or tilting the wings, the aircraft can manipulate the direction of the lift force to turn; the vertical component of lift maintains altitude, while the horizontal component provides the acceleration needed for the turn.