An airplane needs to fly due south. The plane can fly at a speed of 720.0 km/hr in still air. If there is a wind blowing to the northeast at 70.0 km/hr, in what direction should the plane fly to maintain its heading of due south? How long will it take to fly a 1500.0 km distance?

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To determine the direction in which the airplane should fly, we need to consider the effect of both the airplane's speed and the wind on its trajectory.

First, let's break down the speeds into their respective components. The airplane's speed can be broken down into its southern component (the desired direction) and its eastern component (which is perpendicular to the desired direction). Similarly, the wind speed needs to be broken down into its northern component and eastern component.

Given:
- Airplane speed: 720.0 km/hr
- Wind speed: 70.0 km/hr

To find the southern component of the airplane's speed, we need to subtract the northern component of the wind speed from the southern component of the airplane speed. Since the airplane wants to fly south, the southern component of its speed is already negative (-720.0 km/hr).

Southern component of airplane speed = -720.0 km/hr

To find the eastern component of the airplane's speed, we need to add the eastern component of the airplane speed to the eastern component of the wind speed.

Eastern component of airplane speed = 0 km/hr (since the airplane wants to fly due south)

Eastern component of wind speed = 70.0 km/hr (from the given wind speed)

Total eastern component = 0 km/hr + 70.0 km/hr = 70.0 km/hr

Now, let's find the direction in which the airplane should fly. We can use trigonometry to calculate the angle:

tan(θ) = (Eastern component of wind speed) / (Southern component of airplane speed)

tan(θ) = 70.0 km/hr / (-720.0 km/hr)

θ = atan(-70.0 km/hr / 720.0 km/hr)

Using a scientific calculator or an online trigonometry calculator, we find that θ ≈ -5.50 degrees (rounded to two decimal places).

Therefore, the airplane should fly at an angle of approximately 5.50 degrees west of due south to counteract the effect of the wind blowing to the northeast.

To calculate the time it will take for the airplane to fly a distance of 1500.0 km, we can use the equation:

Time = Distance / Speed

Time = 1500.0 km / 720.0 km/hr

Time ≈ 2.08 hours (rounded to two decimal places).

Hence, it will take approximately 2.08 hours to fly a distance of 1500.0 km.