    Question

# The angles of elevation of a balloon from the observer’s eye at two instances are 45º and 60º. If the height of balloon in both the instants is 10 m and it takes (√3−1) seconds, then the approximate speed of the balloon is (Use√3=1.73)

A
4.8 m/s
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B
5 m/s
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C
6.4 m/s
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D
5.8 m/s
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Solution

## The correct option is D 5.8 m/sLet A and E be the positions of the balloon which makes an elevation of 60° and 45° respectively from the observer’s eye at point B. InΔACB, tan60∘=ACBC ⇒√3=10BC ⇒BC=10√3m Similarly,inΔEDB, tan45∘=EDBD ⇒1=10BD (∵ED=AC=10m) ⇒BD=10m Thus,CD=BD−BC=(10−10√3)m Now, time taken by balloon to reach from C to D is (√3−1) seconds. ∴Speedoftheballoon=DistanceTime =10−10√3√3−1 =10(√3−1)√3√3−1 =10√3×√3√3 =10√3√3 =10×1.733 = 5.8 m/s Therefore, the speed of the balloon is 5.8 m/s. Hence, the correct answer is option (d).  Suggest Corrections  0      Similar questions  Explore more