Starting from its nest, an eagle flies at constant speed for 3.0 min due east, then 4.0 min due north. From there the eagle flies directly to its nest at the same speed. How long is the eagle in the air?
ANSWER: STEP 1:- Before answering the question, it’s better to look at the schematic diagram to get some intuition about the problem. The diagram is given below, The diagram below shows the full trajectory of the eagle but not in the units of distance, but in the units of time. As the speed is constant throughout the motion, we should not be worried about the time units. It moved towards east for 3 minutes from it’s nest, then moved towards north for 4 minutes with a constant speed. Then it returned back to it’s nest directly. Everything is shown in the figure and now we will proceed to calculate. STEP 2:- The above figure looks like a right angled triangle with name ABO whose perpendicular and base are 4 and 3 respectively. Sd the segment AB represents the final journey of the eagle, we can find it by the use of pythagoras theorem. 2 2 2 h = p + b -----------------------------------------(1) So, h = b + p = + 4 = 25 = 5 So the eagle travelled for 5 minutes in it’s return journey from A to O. The total amount of time the eagle stayed in air is, 4 min + 3 min + 5 min = 12 minutes CONCLUSION: So the eagle stayed for 12 minutes in air through it’s whole journey.