To determine the height of the balloon when the stone was dropped, we need to calculate the distance the balloon traveled during the stone's fall.
The stone takes 10 seconds to reach the ground, during which time it experiences free fall. In this scenario, the stone's initial velocity is the same as the balloon's ascent rate, which is 30 ft/s (considered positive in this case).
The formula to calculate the distance traveled during free fall is given by:
d = (1/2) * g * t^2
Where: d is the distance g is the acceleration due to gravity (approximately 32.2 ft/s^2) t is the time (10 seconds in this case)
Using this formula, we can determine the distance the stone fell:
d = (1/2) * 32.2 * (10^2) d = 1610 ft
Therefore, the stone fell a distance of 1610 ft. Since the stone was dropped from the balloon, the height of the balloon in that instant is equal to the distance the stone fell. Therefore, the balloon was 1610 ft high when the stone was dropped.