Question : A balloon leaves from point P and rises at a uniform speed. After 6 minutes, an observer situated at a distance of $450\sqrt3$ metres from point P observes that the angle of elevation of the balloon is 60°. Assume that the point of observation and point P is on the same level. What is the speed (in m/s) of the balloon?
Option 1: 4.25
Option 2: 3.75
Option 3: 4.5
Option 4: 3.45
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Correct Answer: 3.75
Solution :
Given: Distance between the observer and the point P is $450\sqrt{3}$ m.
After 6 minutes angle of elevation is 60°.
So, $\tan\theta = \frac{\text{Perpendicular}}{\text{Base}}$
$⇒\tan 60° = \frac{H}{450 \sqrt{3}}$
$⇒\sqrt{3} = \frac{H}{450 \sqrt{3}}$
$\therefore H =450×3 = 1350$ m
Now, for the speed of the balloon,
Speed $=\frac{1350}{6×60}= 3.75$ m/s.
Hence, the correct answer is 3.75.
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