Mabel Breault

2021-12-30

A plane flies directly over a radar station while traveling at $500\frac{mi}{h}$ passes directly over a radar station. Find the rate at which the distance from the plane to the station is increasing when it is 2 mi away from the station.

Finish solving the problem

Jenny Bolton

Beginner2021-12-31Added 32 answers

Note that y is the distance from the plane to the station the problem is referring to.

Differentiate with respect to time t the equation that relates everything.

$x}^{2}+{1}^{2}={y}^{2$

$2x\frac{dx}{dt}+0=2y\frac{dy}{dt}$

$x\frac{dx}{dt}=y\frac{dy}{dt}$

$\frac{x}{y}\frac{dx}{dt}=\frac{dy}{dt}$

We are given that a$\frac{dx}{dt}=500\frac{mi}{h}$ . We also need to find x at the moment $y=2mi$

$x}^{2}+{1}^{2}={2}^{2$

${x}^{2}=4-1=3$

$x=\sqrt{3}$ (ignore negative root)

Plug the values into the differentiated equation.

$\frac{dy}{dt}=\frac{x}{y}\frac{dx}{dt}$

$\frac{\sqrt{3}}{2}\cdot 500$

$250\sqrt{3}\frac{mi}{h}$

Differentiate with respect to time t the equation that relates everything.

We are given that a

Plug the values into the differentiated equation.

levurdondishav4

Beginner2022-01-01Added 38 answers

P is the planes

Vasquez

Expert2022-01-07Added 669 answers

The appropriate diagram here is a right triangle with a short vertical leg of length 1 representing the distance between the station and a point 1 mi directly above it, a longer horizontal leg of variable length x representing the distance from the point above to the position of the plane at time t, and a hypotenuse connecting the plane’s

position with the station (call this distance y). We're told that

Now setting y=2 in the equation

so that

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