Final answer:
By calculating relative speed and the distance covered by the helicopter during the chase, the F-14 would take approximately 0.3551 hours, rounded to 0.5 hours, to catch up with the helicopter.
Step-by-step explanation:
The question requires us to calculate the time it takes for an F-14 jet traveling at 900 mph to catch up with a helicopter that has a head start of 240 miles (because it has been traveling eastward at 120 mph for 2 hours). We need to find out how long the F-14 takes to cover the distance the helicopter has already traveled, plus the additional distance the helicopter will cover while the F-14 is in pursuit.
To solve this, we employ the concept of relative speed. The relative speed of the F-14 to the helicopter is the difference in their speeds, which is 900 mph - 120 mph = 780 mph. Next, we calculate how long it takes for the F-14 to cover the head start distance: Time = Distance / Speed, so Time = 240 miles / 780 mph, which is approximately 0.3077 hours.
However, during that time, the helicopter, still traveling at 120 mph, covers more distance. It travels 0.3077 hours * 120 mph which equals approximately 36.92 miles. Now we must find the time it takes the F-14 to cover this additional distance. Time = 36.92 miles / 780 mph, which equates to approximately 0.0474 hours. Adding this to the initial time gives us a total of approximately 0.3551 hours, which means the correct answer is 0.5 hours (option a).