Answer:
The altitude is changing at a speed of 200 √3 km/hr
Step-by-step explanation:
Here, we want to know how far the altitude of the plane is changing
we are told that the airplane makes an angle of 60 degrees with the ground
So therefore , the rate of change of its altitude will be ;
sin 60 = x/ 400
x = 400 sin 60
x = 400 * √3/2
x = 200 √3 km/hr
The altitude is increasing at a rate of 346.61 km/hr.
The diagram below denotes the given scenario.
Then from the diagram we have,
[tex]sin60^{\circ}=\frac{y}{z}\\\frac{\sqrt{3}}{2} =\frac{y}{z}\\ y=\sqrt{3}\\z=2[/tex]
Then,
[tex]sin\theta =\frac{y}{z}\\cos\theta \frac{d\theta}{dt}\\=\frac{z\frac{dy}{dt}-y\frac{dz}{dt}}{z^2} \\\frac{dy}{dt}=\frac{z^2cos\theta\frac{d\theta}{dt+y\frac{dz}{dt}}}{z}\\\frac{dy}{dt} =\frac{2^2(cos60^{\circ})+\sqrt{3}(400)}{2}\\ \frac{dy}{dt}=346.41 km/hr[/tex]
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