Discussion
A balloon leaves the earth at a point A and rises vertically at uniform speed. At the end of 2 minutes, John finds the angular elevation of the balloon as 60°. If the point at which John is standing is 150 m away from point A, what is the speed of the balloon?
Answer: A
The balloon rises straight up from \( A \), so its height after 2 minutes is the opposite side of a right triangle with base 150 m.
\[ \tan 60^{\circ} = \frac{h}{150} \quad\Longrightarrow\quad h = 150\sqrt{3} = 150 \times 1.732 = 259.8 \text{ m} \]
Two minutes is 120 seconds, so
\[ \text{speed} = \frac{259.8}{120} = 2.165 \approx 2.16 \text{ m/s} \]
Converting the time to seconds before dividing is the step most often missed; dividing by 2 instead gives 129.9 m per minute, which matches none of the options.
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