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A balloon is descending vertically at 4 m/min. From a fixed point on the ground, its angle of elevation is 45°. After 10 minutes, the angle of elevation becomes 30°. How far from the observer will the balloon touch the ground?

1. 20√3 m
2. 20(3+√3) m
3. 10(3+√3) m
4. None of these

Correct answer: 20(3+√3) m

Solution

The balloon descends at a constant rate, and the change in angle of elevation indicates a change in height and horizontal distance. By calculating the height after 10 minutes and using trigonometric relationships, we find the horizontal distance from the observer when the balloon touches the ground, which corresponds to the correct option.

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