Question

Please answer.

An airplane at an altitude of 3000m, flying horizontally at 300km/hr, passes directly over an observer. Find the rate at which it is approaching the observer when it is 5000m away.

Answer 1

Make your sketch, it should be a right-angled triangle

I will assume that the "when it is 5000" refers to the hypotenuse. Make the necessary changes if otherwise.

let the horizontal be 300t, where t is in hrs
the vertical is fixed at 3000
let the hypotenuse be h

when h = 5000
5000^2 =

h^2 = 3000^2 + (300t)^2
when h = 5000
5000^2 = 3000^2 + (300t)^2
300t = 4000
t = 40/3

2h dh/dt = 0 +2(300t)(300)
dh/dt = 90000t/h
= 90000(40/3) / 5000
= 240 km/h