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An aeroplane flying horizontally at height of 2500{3} mts abo

Question

An aeroplane flying horizontally at height of $25003 m t s$ above that ground, is observed to be at angle of elevation $6 0^{o}$ from the ground. After a flight of 25 seconds the angle of elevation is $3 0^{o}$ . Find the speed of the plane in m/sec.

100 m/sec

200 m/sec

300 m/sec.

400 m/sec

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An aeroplane flying horizontally at height of

25003 m t s

above that ground, is observed to be at angle of elevation

6 0^{o}

from the ground. After a flight of 25 seconds the angle of elevation is

3 0^{o}

. Find the speed of the plane in m/sec.

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Text solutionVerified

Let P and Q be the two positions of the aeroplane.

QB = 25003 m t s

Let the speed of the aeroplane be s m/sec.

tan 6 0^{o} = \frac{2500 3}{x}

\frac{2500 3}{x} = 3

x = 2500 m

tan 3 0^{o} = \frac{2500 3}{x + y}

\frac{2500 3}{x + y} = \frac{1}{3}

2500 \times 3 = x + y

7500 = x + y

y = 7500 - 2500

y = 5000 m

To travel 5000 m the aeroplane takes 25 seconds.

The speed of the plane =

\frac{5000}{25} = 200

m/sec

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Question Text	An aeroplane flying horizontally at height of $25003 m t s$ above that ground, is observed to be at angle of elevation $6 0^{o}$ from the ground. After a flight of 25 seconds the angle of elevation is $3 0^{o}$ . Find the speed of the plane in m/sec.
Answer Type	Text solution:1
Upvotes	150