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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 (31) seconds, then the approximate speed of the balloon is (Use3=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/s
Let 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=103m
Similarly,inΔEDB,
tan45=EDBD
1=10BD (ED=AC=10m)
BD=10m
Thus,CD=BDBC=(10103)m
Now, time taken by balloon to reach from C to D is (31) seconds.
Speedoftheballoon=DistanceTime
=1010331
=10(31)331
=103×33
=1033
=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).

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