can you answer this question ?

Question

An airplane, flying at 455 km/h at a constant altitude h = 6 km, is approaching a camera on the ground. Let q be the angle of elevation above the ground at which the camera is pointed. When q = π /4 how fast does the camera have to rotate in order to keep the plane in view?( after getting the answer invert it in terms of radians/ hour)

Answer 1

It isn't same every second!

But I shall answer as far as I know!

Let v be the velocity per second of plane!
next, Let d be the distance between cameras and projected plane on the ground!
Let t be the time in second!
and Let r be the angle to work out!
and f is the function to work out the rotated angle with parameter as time!

v=455/3600=0.1264km/s
h=6km
since r=pi/4 , d=6km
and dt=6-vt

and f(t)=arctan(h/d)-pi/4=
=arctan(6/(6-0.1264t))-pi/4

solution:
f(t)=arctan(6/(6-0.1264t))-pi/4
parameter t is time in second
and output is rotated angle!

wishing you be happy with this answer

Answer 2

Draw a picture.
Make a right triangle with the plane and camera as two points, A verticle line from the camera and a horizontal line from the plane

p-----
..\....|
....\..|
.....\.|
.......c

Relate the top leg of the triangle with the angle.

Hint
an angle of the triangle is the same as the horizon angle from the theorm of alternate interior angles of parallel lines.

Another Hint
the altitude is a constant and is needed for the derivative.

Now the derivative of the top segment is the velocity of the plane. The deirvative of the elevation angle is what you want.

I hope you are in a calculus class

Answer 3

First work out the speed of that airplane per second...

Speed(1s)=455000/3600=126.39m

the distance from camara to the phase-point of plane is
6000 m (because q = π /4 and h=6km...)

So the distance between c.. and p-p-p after 1s is...
d=6000-Speed(1s)=5873.61

so, q(t)=arctan(h/d)- π /4=45.61-45=0.61'=0.0213 rad/second

you want radians/hour...

I don't think it's available...

If you say one hour, the plane would disappear from camara...

Answer 4

no