The angle of the elevation of a lie plane a point A on the ground is 60∘ . After a flight of 30 seconds, the angle of the elevation changes to 30∘. If the jet plane is flying at a constant height of 36003 m, find a speed of the jet plane.

Question

The angle of the elevation of a lie plane a point A on the ground  is 60∘ . After a flight  of 30 seconds, the angle of the elevation changes to 30∘. If the jet plane is flying at a constant height of 36003​ m, find a speed of the jet plane.

Filo · Accepted Answer

Let P and Q be the two positions of the plane and Let 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 600 and 300 respectively.Therefore, ∠PAB=600 and ∠QAB=300 It is also given that PB=36003​ metres.In ΔABP,  tan600=ABBP​⟹3​=AB36003​​⟹AB=3600mIn ΔACQ,  tan300=ACCQ​⟹3​1​=AC36003​​⟹AC=3600×3=10800mTherefore, PQ=BC=AC−AB=10800−3600=7200mThus the plane travels 7200m in 30 seconds.Hence, the speed of the plane is 307200​=240m/sec=240×100060∗60​=864km/hr

Question Text	The angle of the elevation of a lie plane a point A on the ground is $6 0^{\circ}$ . After a flight of 30 seconds, the angle of the elevation changes to $3 0^{\circ}$ . If the jet plane is flying at a constant height of $36003$ m, find a speed of the jet plane.
Answer Type	Text solution:1
Upvotes	150

The angle of the elevation of a lie plane a point A on the ground is $6 0^{\circ}$ . After a flight of 30 seconds, the angle of the elevation changes to $3 0^{\circ}$ . If the jet plane is flying at a constant height of $36003$ m, find a speed of the jet plane.

Text solutionVerified

Practice questions from similar books

The angle of the elevation of a lie plane a point A on the ground is 60∘ . After a flight of 30 seconds, the angle of the elevation changes to 30∘. If the jet plane is flying at a constant height of 36003​ m, find a speed of the jet plane.

Text solutionVerified

Practice questions from similar books

The angle of the elevation of a lie plane a point A on the ground is $6 0^{\circ}$ . After a flight of 30 seconds, the angle of the elevation changes to $3 0^{\circ}$ . If the jet plane is flying at a constant height of $36003$ m, find a speed of the jet plane.