To understand why a flying object needs to achieve escape velocity to leave the Earth's atmosphere, it's important to grasp the concept of gravitational potential energy and the balance between gravitational force and kinetic energy.
Escape velocity refers to the minimum speed an object must attain to escape the gravitational pull of a celestial body, such as the Earth. This velocity is determined by the mass and radius of the body. In the case of the Earth, the escape velocity is about 11.2 kilometers per second (or approximately 25,020 miles per hour).
When an object is within the Earth's gravitational field, it experiences a gravitational force pulling it towards the center of the planet. As the object gains altitude, it moves away from the Earth's surface, and the gravitational force weakens due to the inverse square law. However, the object's potential energy increases as it moves further away from the planet's center.
As the object gains altitude, it also converts some of its kinetic energy (energy associated with its motion) into potential energy. If the object slows down, it loses kinetic energy and its potential energy increases even further. Eventually, at a certain altitude, the object's kinetic energy will be completely converted into potential energy, and it will come to a stop before falling back towards the Earth under the influence of gravity.
To escape the Earth's gravitational field, the object needs enough kinetic energy to overcome the increasing potential energy and counteract the gravitational pull. Achieving escape velocity ensures that the object can continue moving away from the Earth without being pulled back.
In practical terms, this means that a flying object must achieve a minimum speed to overcome Earth's gravitational pull and keep moving away. Going at a slower speed would not provide enough kinetic energy to counterbalance the increasing potential energy, and the object would ultimately be pulled back to the Earth's surface.
Therefore, to successfully leave the Earth's atmosphere, a flying object needs to attain escape velocity to counteract the gravitational forces acting upon it and continue moving away from the planet.