A balloon leaves the earth at a point A and rises vertically at uniform speed At the end of 2 minute...........

Quantitative Aptitude ( CCS) Trignometry

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?

0.63 meter/sec

2.16 meter/sec

3.87 meter/sec

0.72 meter/sec

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Explanation:

Let C be the position of John. Let A be the position at which balloon leaves the earth and B be the position of the balloon after 2 minutes.
Given that CA = 150 m, angleBCA = 60°
tan60°=BA/CA
√3=BA/150
BA=150√3
i.e, the distance travelled by the balloon =150√3meters
time taken = 2 min = 2 × 60 = 120 seconds
Speed =Distance/Time
=150√3/120
=1.25√3
=1.25×1.73
=2.16 meter/second