Neglecting air resistance, a ball thrown horizontally with a certain velocity from 10 floors up a building will hit the ground at twice the distance from the building as if it were thrown from 5 floors up.

Question

Quizplus · Accepted Answer

Neglecting air resistance, the horizontal distance a projectile travels is determined by its initial horizontal velocity and the time it is in the air. The time in the air is determined by the vertical component, which depends on the height from which it is dropped. Doubling the height does not double the time in the air since the time to fall is proportional to the square root of the height (from the equation $t = \sqrt{\frac{2h}{g}}$), so the ball thrown from 10 floors up will not hit the ground at twice the distance from the building as if it were thrown from 5 floors up.

Neglecting Air Resistance, a Ball Thrown Horizontally with a Certain