Final answer:
During takeoff, the aircraft's engines provide horizontal force through propulsion and vertical force by wing design, which creates lift by pushing air downwards and backwards.
Step-by-step explanation:
The thrust of an aircraft's engine provides both vertical and horizontal forces during takeoff. The horizontal force is generated primarily through the propulsion mechanism of the engine, such as the jet thrust or propellers pushing against the air, propelling the aircraft forward. However, during takeoff, the aircraft's engines and wings are angled in such a way that they also provide a vertical force. This is not because of gravity, but rather due to the design of the wings which create lift by forcing air downwards and backwards, similar to how birds achieve lift. When an airplane banks, it achieves a balance of vertical force to counteract its weight and a horizontal force to facilitate the turn, all achieved through the manipulation of lift.