A) \[785.46\text{ }km/hr\]
B) \[790.56\text{ }km/hr\]
C) \[780.56\text{ }km/hr\]
D) \[782.65\text{ }km/hr\]
Correct Answer: B
Solution :
Let the point on the ground is E which is y metres from point B and let after 10 sec. flight it covers x metres distance. In \[\Delta \,\,AEB,\] \[\tan \,{{45}^{o}}=\frac{AB}{EB}\,\Rightarrow 1=\frac{3000}{y}\Rightarrow \,y=3000\,m\] ?...(1) In \[\Delta CED,\] \[\tan \,{{30}^{o}}=\frac{CD}{ED}\Rightarrow \frac{1}{\sqrt{3}}=\frac{3000}{x+y}\] \[(AB\,=\,CD)\] \[\Rightarrow \] \[x+y=3000\sqrt{3}\] .....(2) From equation (1) and (2), we have \[x+3000=3000\sqrt{3}\] \[\Rightarrow \] \[x=2196\,m\] Speed of aeroplane \[=\frac{Distance\text{ }covered}{Time\text{ }taken}\] \[=\frac{2196}{10}\times \frac{18}{5}km/hr=790.56km/hr\] Hence, the speed of aeroplane is \[790.56\text{ }km/hr.\]You need to login to perform this action.
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