A rocket is launched at the rate of 11 feet per second from a point on the ground 15 feet from an observer. To 2 decimal places in radians per second, find the rate of change of the angle of elevation when the rocket is 30 feet above the ground.

Accepted Solution

let the angle of elevation is x and the height of the rocket from the ground is y

tanx = y/15

by differentiating both sides with respect to T

sec²x·dx/dt = (dy/dt)/15

at y = 30 , the hypotenuse of the triangle = 15√5


5 dx/dt = 11/15

dx/dt = 11/75 rad/sec