Airplane

Calculus Level 2

An airplane is flying horizontally at an altitude of 9000 m. An observer on the ground noticed that when the angle of elevation of the plane is 60 degrees, the angle decreases at the rate of 0.15 radians / second. What is the velocity of the airplane in m/s?

1800 m/s 2000 m/s 1900 m/s 1700 m/s

1 solution

A Former Brilliant Member
Oct 26, 2016

when A = 60 degrees; dA/dt = -0.15 rad/sec

tan A = 9000/x

x = 9000/tan A = 9000 cotA

$\frac{dx}{dt}$ $=$ $9000$ $(-csc^2A\frac{dA}{dt})$

$\frac{dx}{dt}$ $=$ $-9000$ $(csc^260)$ $(-0.15)$ $=$ $1800$ $m/s$

Airplane

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