An airplane is flying such that its altitude and horizontal distance (both in meters)…

MATHEMATICS · Single correct · CBSE · Mathematics · Applications of Derivatives · Applications of Derivatives

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}