Final Answer:
The path of a projectile on Earth is curved like a parabola.
Step-by-step explanation:
When an object is launched into the air on Earth without any additional propulsion after its release, it follows a path known as a projectile motion. This path is a result of the combination of its initial horizontal velocity and the constant vertical acceleration due to gravity.
The key factor in this motion is that the horizontal component of velocity remains constant, while the vertical component changes due to gravity. As a result, the trajectory formed by the object is a curve known as a parabola.
Initially, the object moves horizontally with a constant velocity, but gravity acts vertically downward, causing the vertical velocity to decrease until it reaches its peak and then starts increasing as it falls back down. The combined effect of these velocities creates a curved path, which, when graphed, forms a parabolic shape.
This behavior can be mathematically represented by equations of motion derived from the laws of physics, where the horizontal distance traveled is proportional to the horizontal velocity and the time elapsed, while the vertical distance follows a quadratic relationship due to the constant acceleration from gravity.
The parabolic trajectory of a projectile on Earth can be described using equations like the range equation, which determines how far the projectile travels horizontally before hitting the ground. Understanding and analyzing this motion involve concepts from kinematics and calculus, utilizing equations that consider both horizontal and vertical components of motion along with the effects of gravity to accurately predict and describe the path of a projectile on Earth as a curved trajectory in the shape of a parabola.