Question

Kylo Ren's shuttle is landing on a planet by descending vertically. Their altitude after t seconds is given by the function h (t ) 30000 * 6000sqrt(t). They are interested in finding Poe Dameron who they believe is hiding in a village that they are looking at through a window on their shuttle. The village is 300 feet from the landing site. Find the rate of change of the angle of depression when the straight-line distance from the shuttle to the village is 500 feet.

Answer 1

The problem requires finding the rate of change of the angle of depression when the straight-line distance from the shuttle to the village is 500 feet. The angle of depression is the angle between the horizontal and the line of sight from an observer to a lower object. To find the rate of change of the angle of depression, you would need to determine the derivative of the angle with respect to time and then use the Pythagorean theorem to find the distance between the shuttle and the village. Then, you would use trigonometry to find the angle of depression. The final step would be to find the derivative of the angle of depression with respect to time to find the rate of change of the angle of depression.