Question

the angle of elevation of a jet plane from a point A on the ground is 60° after 15 sec The angle of elevation changes to 30° if the plane is flying at a constant height of 1500root3 ms find the speed of jet plane

Answer 1

Let D and E be the initial and final positions of the plane respectively


Consider the triangle ABD
tan60=BDAB√3=1500√3ABAB=1500tan⁡60=BDAB3=15003ABAB=1500


Consider the triangle ACE
tan30=CEAC1√3=1500√3ACAC=4500tan⁡30=CEAC13=15003ACAC=4500


BC = AC - AB = 4500 - 1500 = 3000 m
DE = BC = 3000 m

i.e., the plan travels a distance of 3000 m in 15 seconds.
Therefore, speed of the plane =300015=300015 = 200 m/s