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n aeroplane fying horizontally at a height of 1.5above the grond is oerved at a certain point on theearth to suhtend an angle of 60 Afer 15 seconds, isangle of elevation is ofserved to be 30 calculate thespeed of aero plane in kmhr. |
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Answer» [IN DIAGRAM, BC = ED = 1500 m. It is not 2500m. It is an error. I regret for the inconvenience] In ∆ABC,cot 60° = AC/BC=> 1/√3 = AC/1500=> AC = 1500/√3 ....(i) In ∆AED,cot 30° = AE/ED=> √3 = AE/1500=> AE = 1500√3 ....(ii) From figure,BD = CEand, CE = AE - ACso, BD = AE - AC Now, substituting value of AE and AC from equations (i) and (ii),BD = 1500√3 - 1500/√3= 1500 (√3 - 1/√3)= 1500 × 2/√3BD = 3000/√3 BD is covered by the aeroplane in 15 seconds. So,Speed of Aeroplane = Distance (BD) ÷ Time (t)= 3000/√3 ÷ 15 m/sec= 3000/ (15 × 1.732) m/sec= 115.473 m/sec Hence, speed of the aeroplane is 115.473 m/sec |
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