From a point on the ground, the angle of elevation of an aeroplane flying at an altitude of 500m change from `45^(@) " to " 30^(@)` in 5 seconds. Find the speed of the aeroplane ( in kmph).

Options

A. `243.52` km/s
B. `253.52` km/s
C. `263.52` km/s
D. `273.52` km/s

Answer

C

Explanation

Let A and B be the initial and final positions of the plane.
Given, AQ=500 m
`thereforeBR=500m (AQ=BR)`

In `Delta APQ`,
`tan45^(@)=(AQ)/(PQ)`
`1= (500)/(pq)`
`therefore PQ` = 500 m.
In `DeltaBPR`,
`tan30^(@)=(BR)/(PR)`
`(1)/(sqrt3)=(500)/(PQ+QR)rArr500+QR=500sqrt3`
`QR=500(sqrt3-1) mthereforeAB=500(sqrt3-1)m`.
Speed of the plane `=(AB)/(Time)`
`=((500(sqrt3-1))/(5))m//s`
`=100(sqrt3-1)((18)/(5))kmph`
`=360(sqrt3-1)kmph`