Homework SourseAn airplane flies at an altitude of 2 miles toward a point d
An airplane flies at an altitude of 2 miles toward a point directly over an observer. The speed of the plane is 500 miles per hour. Find the rates at which the angle of elevation ? is changing when the angle is ? = 45
Solution
cot = 500t/2
cot = 250t
-csc² d/dt = 250
d/dt = 250(-1/csc²)
d/dt = -250sin²
at = 45deg
d/dt = -250sin²(45)
= -250(2/2)²
= -250(2/4)
= -125 rad/hr
at =60deg
d/dt = -250sin²(60)
= -250(3/2)²
= -250(3/4)
= -187.5 rad/hr
at = 80deg
d/dt = -250sin²(80)
= -242.46 rad/hr
the negative rates just means the angle of elevation is decreasing.
