What is the shape of the trajectory for a projectile launched in a vacuum near the Earth's surface?

Parabolic. In a vacuum near the Earth's surface, where gravity is the only significant force acting on a projectile, the trajectory of a launched object will follow a parabolic path. This shape emerges from the combination of the constant acceleration due to gravity acting downwards and the initial velocity of the projectile, which can be resolved into horizontal and vertical components. The horizontal velocity remains constant while the vertical velocity changes due to gravity, creating the characteristic curved, parabolic path. In real-world situations with air resistance, the trajectory may deviate from a perfect parabola due to additional drag forces acting on the object, but in a vacuum, the ideal parabolic shape is preserved.