Answer:
The angle of elevation of the rocket is increasing at a rate of 48.780º per second.
Explanation:
Geometrically speaking, the distance between the rocket and the observer (
), measured in kilometers, can be represented by a right triangle:
(1)
Where:
- Horizontal distance between the rocket and the observer, measured in kilometers.
- Vertical distance between the rocket and the observer, measured in kilometers.
The angle of elevation of the rocket (
), measured in sexagesimal degrees, is defined by the following trigonometric relation:
(2)
If we know that 
, then the expression is:
And the rate of change of this angle is determined by derivatives:
Where:
- Rate of change of the angle of elevation, measured in sexagesimal degrees.
- Vertical speed of the rocket, measured in kilometers per hour.
If we know that 
and 
, then the rate of change of the angle of elevation is:
The angle of elevation of the rocket is increasing at a rate of 48.780º per second.
