An aeroplane flying horizontally at a height of 3 km. above the g
| An aeroplane flying horizontally at a height of 3 km. above the ground is observed at a certain point on earth to subtend an angle of 60°. After 15 sec flight, its angle of elevation is changed to 30°. The speed of the aeroplane (taking √3 = 1.732) is:
A. 230.63 m/sec
B. 230.93 m/sec
C. 235.85 m/sec
D. 236.25 m/sec
Please scroll down to see the correct answer and solution guide.
Right Answer is: B
SOLUTION
Short Trick:
√3 unit = 3000 m
1 unit = 1000√3
2 unit = 2000√3 = 2000 × 1.732 = 3464 m
Distance covered by plane in 15 sec = 3464 m
∴ Speed of the plane = 3464/15 = 230.93 m/sec
Detailed Method:
AD = BC = 3 km = 3000 m
In ΔPDA
tan 60 = AD/PA
⇒ √3 = 3000/PA
⇒ PA = 1000√3
In ΔPCB
tain30 = BC/PB
⇒ 1/√3 = 3000/PB
⇒ PB = 3000√3
AB = PB - PA
AB = 3000√3 - 1000√3 = 2000√3 = 2 × 1.732 = 3464 m
Distance covered by plane in 15 sec = 3464 m
∴ Speed of the plane = 3464/15 = 230.93 m/sec