If we ignore air resistance, the height a ball can reach when thrown straight up depends on the initial velocity with which it is thrown. The ball will rise until its upward velocity decreases to zero, at which point it will start to fall back down due to the force of gravity.
The maximum height reached by the ball can be calculated using the laws of motion. At the highest point, the ball's velocity will be zero, and its potential energy will be maximized. Assuming the acceleration due to gravity is constant (approximately 9.8 m/s² near the Earth's surface), the maximum height (h) can be determined using the following equation:
h = (v₀²) / (2g)
Where:
- h is the maximum height reached
- v₀ is the initial velocity (upward velocity)
- g is the acceleration due to gravity
Keep in mind that if the ball is thrown with a velocity greater than the escape velocity of Earth (which is about 40,270 km/h or 11.2 km/s), it will have enough kinetic energy to overcome Earth's gravitational pull and could potentially leave the Earth's atmosphere altogether. However, reaching such high velocities would require an extremely powerful throw or propulsion system.