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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
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
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