To find the time interval required for the jetliner to complete the trip in each scenario, we need to use the formula:
Time = Distance / Speed
(a) With a headwind of 41.1 km/h towards the north:
The speed of the jetliner relative to the ground would be:
Speed = Jetliner's airspeed - Headwind speed
Speed = 597.4 km/h - 41.1 km/h = 556.3 km/h
The distance traveled is 780.1 km.
So, the time interval required is:
Time = Distance / Speed
Time = 780.1 km / 556.3 km/h
Time ≈ 1.400 hours (rounded to three decimal places)
Therefore, the time interval required to complete the trip with a headwind of 41.1 km/h is approximately 1.400 hours.
(b) With a tailwind of the same speed (41.1 km/h):
The speed of the jetliner relative to the ground would be:
Speed = Jetliner's airspeed + Tailwind speed
Speed = 597.4 km/h + 41.1 km/h = 638.5 km/h
Using the same distance (780.1 km), the time interval required is:
Time = 780.1 km / 638.5 km/h
Time ≈ 1.221 hours (rounded to three decimal places)
Therefore, the time interval required to complete the trip with a tailwind of 41.1 km/h is approximately 1.221 hours.
(c) With a crosswind of the same speed (41.1 km/h) towards the west:
The crosswind does not affect the jetliner's speed along the southward direction. As a result, the previous speed remains the same:
Speed = 597.4 km/h
Using the same distance (780.1 km), the time interval required is:
Time = 780.1 km / 597.4 km/h
Time ≈ 1.305 hours (rounded to three decimal places)
Therefore, the time interval required to complete the trip with a crosswind of 41.1 km/h towards the west is approximately 1.305 hours.