Home
Class 10
MATHS
The angle of elevation of an aeroplane f...

The angle of elevation of an aeroplane from a point P on the ground is `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 sqrt3` m, find the speed of the aeroplane

Text Solution

Verified by Experts

Let OX be the horizontal ground and let O be the point of observation. Let A and B be the two positions of the aeroplane.
Let `AC_|_ OX` and `BD _|_ OX`. Then,
`angleCOA = 60^(@), angleDOB = 30^(@)`.
and `AC = BD = 1500sqrt(3) m`.
From right `DeltaOCA`, we have
`(OC)/(AC) = cot 60^(@) = 1/(sqrt(3))`.
`rArr (OC)/(1500sqrt(3)) = 1/(sqrt(3)) rArr OC = 1500 m`.
From right `DeltaODB`, we have
`(OD)/(BD)= cot 30^(@) = sqrt(3) rArr(OD)/(1500sqrt(3m)) = sqrt(3)`.
`rArr OD = (1500 xx 3) m = 4500 m`.
`:. CD = (OD - OC) = (4500 - 1500) m = 3000 m`.
Thus, the aeroplane covers `300 m` in `15` seconds.
`:.` speed of the aeroplane `= (3000/15 xx (60xx60)/(1000))km//hr`
`= 720 km//hr`.
Hence, the speed of the aeroplane is `720 km//hr`.
Promotional Banner

Similar Questions

Explore conceptually related problems

The angle of elevation of an aeroplane from a point P on the ground is 60. After a flight of 15 seconds,the angle of elevation changes to 30 . If the aeroplane is flying at a constant height of 15003m, find the speed of the aeroplane.

The angle of elevation of an airplane from a point on the ground is 60^(@) . After a flight of 30 seconds, the angle of elevation becomes 30^(@) . If the airplane is flying at a constant height of 3000sqrt(3) m, find the speed of the airplane.

The angle of elevation of a jet plane from a point A on the grund is 60^(@). After and flight of 30 seconds,the angle of elevation changes to 30^(@). If the jet plane is flying at a constant height of 3600sqrt(3)m, find the speed of the jet plane.

The angle of elevation of a jet plane from a point A on the ground is 60o .After a flight of 30 seconds,the angle of elevation changes to 30o. If the jet plane is flying at a constant height of 3600sqrt(3)m, find the speed of the jet plane.

The angle of elevation of the top of a building from the foot of the tower is 60^(@) . After a flight of 15 seconds, the angle of elevation changes to 30^(@) . If the aeroplane is flying at a constant height of 1500sqrt3 m find the speed of the plane in km/hr.

The angle of elevation of a jet plane from a point A on the ground is 60^(@). After a flight of 15 seconds,the angle of elevation changes to 30^(@). If the jet plane is flying at a constant height of 1500sqrt(3) meter,find the jet plane.(sqrt(3)=1.732)

The angle of elevation of an aeroplane from a point on the ground is 60^(@) .After flying for 30 seconds ,the angle of elevation changes to 30^(@) .If the aeroplane is flying at a height of 1500sqrt(3) metre , then what is the speed (in m/s) of aeroplane?

The angle of elevation of an aeroplane from a point on the ground is 60^(@) . After flying for 30 seconds, the angle of elevation charges to 30^(@) . If the aeroplane is flying at a height of 4500 m, then what is the speed (in m/s) of aeroplane

The angle of elevation of an aeroplane from a point on the ground is 60^@ . After flying for 30 seconds, the angle of elevation changes to 30^@ . If the aeroplane is flying at a height of 4500 m,then what is the speed (in m/s) of aeroplane? मैदान पर एक बिन्दु से एक हवाई जहाज का उन्नयन कोण 60^@ है। 30 सेकण्ड उड़ने के पश्चात कोण 30^@ में परिवर्तित हो जाता हे। यदि हवाई जहाज 4500 मी. की ऊँचाई पर उड़ रहा है, तो हवाई जहाज की गति (मी./से. में) क्या है?

The angle of the elevation of an aeroplane from a point on the ground is 45^(@) . After flying for 15 seconds, the elevation changes to 30^(@) . If the aeroplane is flying at a height of 2500 metres. Find the speed of the aeroplane.