Question

A projectile is fired vertically from the surface of the Earth at 8km/s. This projectile will (go into circular motion about the Earth, rise and fall back to the Earth's surface, follow an uncertain path)

Answer 1

A projectile fired at 8 km/s from Earth's surface will go into circular motion around the Earth, achieving orbit due to reaching the circular satellite velocity.

Step-by-step explanation:

The question involves determining the path of a projectile that is fired vertically at a speed of 8 km/s from the Earth's surface. Given the speed, the projectile is near the speed necessary to achieve orbit. This is known as the circular satellite velocity, which is approximately 8 kilometers per second or about 17,500 miles per hour. At this speed, the Earth's curvature drops away at the same rate that gravity pulls the projectile downwards, allowing it to fall around the Earth continuously without hitting the surface. Therefore, this projectile will go into circular motion around the Earth, assuming ideal conditions without air resistance and other perturbations.