If you were to throw a ball horizontally, neglecting air resistance, it would follow a curved trajectory due to Earth's gravitational pull. The distance it would travel before hitting the ground depends on several factors such as the initial velocity of the ball, the angle at which it is thrown, and the radius of the Earth.
Assuming a flat, level surface and neglecting air resistance, the ball would travel in a projectile motion. The time it takes for the ball to hit the ground would depend on the vertical component of its initial velocity. The horizontal component of the initial velocity would determine how far the ball would travel horizontally before hitting the ground.
Let's consider an example where the ball is thrown with an initial velocity of 10 meters per second at an angle of 45 degrees with respect to the horizontal. In this case, the horizontal component of the velocity would be 10 m/s multiplied by the cosine of 45 degrees, which is approximately 7.07 m/s.
Assuming the radius of the Earth is approximately 6,371 kilometers (or 6,371,000 meters), we can calculate the time it would take for the ball to hit the ground using the vertical motion equation:
h = (1/2) * g * t^2
Where: h is the initial height of the ball (considered negligible for this example) g is the acceleration due to gravity (approximately 9.8 m/s^2) t is the time it takes for the ball to hit the ground
Using this equation, we can solve for t:
0 = (1/2) * 9.8 * t^2
Simplifying the equation, we find:
t^2 = 0 t = 0
From the equation, we can see that the ball would hit the ground instantaneously. However, this is not physically accurate because we are neglecting air resistance, which would cause the ball to fall in a curved path.
To summarize, the distance from Earth at which a ball would hit the ground depends on various factors such as the initial velocity, angle of projection, and the radius of the Earth. The calculation becomes more complex when considering the effects of air resistance and the curvature of the Earth. In practice, the distance the ball would travel before hitting the ground would be relatively short due to the gravitational pull and the curved trajectory it would follow.