Final answer:
The pilot's speed is calculated using the change in angle of depression and the constant altitude of 2000 m. With the angles provided and without using a calculator, the speed is found to be 540 km/h.
Step-by-step explanation:
The student's question involves calculating the pilot's speed based on the angle of depression changes. First, we notice that the angle of depression changes from 45° to 75', the latter of which should be degrees (75°). Assuming this is a typo, because 75' (minutes) is a subdivision of degrees and it does not make sense in this context. With a 45° angle of depression and a height of 2000 m, the initial distance to the camp is equal to the height (due to the 1:1 ratio of a 45° right triangle). After 10 seconds, the new angle of depression is 75°, and we can use the tangent function to find the new horizontal distance:
tan(75°) = 2000 m / x
Since tan(75°) is approximately 4 (because it's a known value that tan(75°) is about 3.73, and we are not using a calculator), we rewrite this as:
4 = 2000 m / x
Solving for x gives us x = 500 m. The pilot has therefore traveled 2000 m - 500 m = 1500 m in 10 seconds. To convert this to km/h, we use the fact that 1500 m = 1.5 km, and 10 seconds is 1/360 hour.
Thus, speed = distance/time = 1.5 km / (1/360 h) = 1.5 km * 360 = 540 km/h.