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JEE Main 201815 April
Exam
JEE Main
Year
2018
Date
15 April
Subject
Mathematics
Chapter
Heights and Distances

JEE Main 2018 · 15 April · Mathematics · Heights and Distances

An aeroplane flying at a constant speed, parallel to the horizontal...

An aeroplane flying at a constant speed, parallel to the horizontal ground, 3km\sqrt{3}km above it is observed at an elevation of 60°{60}^{°} from a point on the ground. If after five seconds, its elevation from the same point is 30°{30}^{°}, then the speed (in km/hrkm / hr) of the aeroplane isAn aeroplane flying at a constant speed, parallel to the horizontal ground, 3 km above it is observed at an elevation

Options

  1. A720720
  2. B15001500
  3. C750750
  4. D14401440

Correct answer

D. 14401440

Step-by-step solution

An aeroplane flying at a constant speed, parallel to the horizontal ground, 3 km above it is observed at an elevationLet from point CC the angle of elevation of plane at BB is 60°{60}^{°}.

and after 55 seconds it reach at B′{B}^{'}

In ∆ABC,AC=3cot60°=1∆ ABC, AC = \sqrt{3}cot{60}^{°} = 1

In \DeltaCA′B′,A′C=3cot30°=3\DeltaC{A}^{'}{B}^{'}, {A}^{'}C = \sqrt{3}cot{30}^{°} = 3

Hence, distance AA′=A′C−AC=3−1=2A{A}^{'} = {A}^{'}C - AC = 3 - 1 = 2

Now, speed equals total distance travelled divided by total time taken.

Thus, speed =2560×60=2×60×605=72005=1440km/hr= \dfrac{2}{\dfrac{5}{60 \times 60}} = \dfrac{2 \times 60 \times 60}{5} = \dfrac{7200}{5} = 1440km / hr

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