Question

The angle of elevation of an aeroplane from a point A on the ground 60°. After a flight of 15 seconds, the angle of elevation changes to 30°. If the aeroplane is flying at a constant height of $1500 space square root of 3 space end root space straight m$ , find the speed of the plane in km/hr.

Solution

Let P and Q be the two positions of the plane and A be the point of observation. Let ABC be the horizontal line through A. It is given that angles of elevation of the plane in two positions P and Q from a point A are 60° and 30°, respectively.

∴ ∠PAB = 60^o and ∠QAC = 30^o

Also comma space PB space equals space QC space equals space 1500 square root of 3 space straight m In space increment ABP comma space we space have tan space 60 degree space equals space BP over AB rightwards double arrow space square root of 3 space equals space fraction numerator 1500 square root of 3 over denominator AB end fraction rightwards double arrow space AB space equals space 1500 space straight m In space increment ACQ comma space we space have space tan space 30 degree space equals space QC over AC rightwards double arrow space fraction numerator 1 over denominator square root of 3 end fraction space equals space fraction numerator 1500 square root of 3 over denominator AB end fraction rightwards double arrow space AC space equals space 1500 space straight x space 3 space equals space 4500 space straight m therefore space BC space equals space AC space minus space AB space equals space 4500 space straight m space minus space 1500 space straight m space equals space 3000 space straight m Thus comma space the space plane space travels space 3000 space meters space in space 15 space second. therefore space Speed space space of space the space plane equals space 3000 over 15 equals space 20 space straight m divided by straight s space equals space fraction numerator 200 space straight x space 60 space straight x space 60 space over denominator 1000 end fraction equals 720 space km divided by straight h Hence comma space the space speed space of space the space plane space is space 720 space km divided by straight h.

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Circles

The angle of elevation of an aeroplane from a point A on the ground 60°. After a flight of 15 seconds, the angle of elevation changes to 30°. If the aeroplane is flying at a constant height of $1500 space square root of 3 space end root space straight m$ , find the speed of the plane in km/hr.

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The angle of elevation of an aeroplane from a point A on the ground 60°. After a flight of 15 seconds, the angle of elevation changes to 30°. If the aeroplane is flying at a constant height of , find the speed of the plane in km/hr.

Some More Questions From Circles Chapter

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The angle of elevation of an aeroplane from a point A on the ground 60°. After a flight of 15 seconds, the angle of elevation changes to 30°. If the aeroplane is flying at a constant height of $1500 space square root of 3 space end root space straight m$ , find the speed of the plane in km/hr.