Question

An airplane is flying on a flight path that will take it directly over a radar tracking station. If the distance between the tracking station and the airplane is decreasing at a rate of 400 miles per hour when the distance between them is 10 miles, what is the speed of the plane if the plane is always 3 miles above the ground?

Answer 1

Answer:

The speed of planes is 419.31 miles per hours

Explanation:

Given that

$\dfrac{dS}{dt}=-400\ miles/hr$

S= 10 miles

And we have to find $\dfrac{dx}{dt}$.

From triangle ABC

$AC^2=AB^2+BC^2$

$S^2=x^2+3^2}$

by differentiating with respect to time t

$2S\dfrac{dS}{dt}=2x\dfrac{dx}{dt}$

$S\dfrac{dS}{dt}=x\dfrac{dx}{dt}$

Now when S=10 miles then

$10^2=x^2+3^2}$

x= 9.53 miles

So

$S\dfrac{dS}{dt}=x\dfrac{dx}{dt}$

$10\times (-400)=9.53\times \dfrac{dx}{dt}$

$\dfrac{dx}{dt}=-419.31\ miles/hr$

So the speed of planes is 419.31 miles per hours