Mathematics

Mathematics

Problem

An airplane is flying such that its altitude

h

and horizontal distance

x

(both in meters) from a radar station satisfy

\theta = \arctan\!\left(\dfrac{h}{x}\right)

. At a certain instant

h=1000

,

x=3000

,

\dfrac{dh}{dt}=150\,\text{m/s}

, and

\dfrac{d\theta}{dt}=0.020\,\text{rad/s}

. What is the airplane’s horizontal speed

\dfrac{dx}{dt}

at that instant? a)

270\,\text{m/s}

b)

250\,\text{m/s}

c)

450\,\text{m/s}

d)

260\,\text{m/s}

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