An aircraft is flying at a uniform speed v m/s. If the angle subtended at an observation point on the ground by two positions of the aircraft f second apart is θ, the height of the aircraft above the ground is given by
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a
vt2tanθ
b
2vttanθ
c
vttan(θ/2)
d
vt(2tanθ/2)
answer is D.
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Detailed Solution
See figure. In figure P and Q are two positions of the aircraft f seconds apart respectively. ∴PQ=vt or RQ=(vt/2)From ΔORQtanθ2=RQOR=(vt/2)h∴h=vt2tan(θ/2)