I am flying a plane capable of an airspeed of 100 km/hr.

If the wind velocity was 45 km/h [95], in what direction would I have to fly in order to follow the track to my destination. And how long would this trip take? The distance between my starting point and my destination is 137.25 km.

unless you give the destination's direction, there's no way to answer that. If it's 137.25 [95], then just add airspeed + windspeed and divide

If it's 137.25 [275] the subtract wind speed from airspeed.

etc.

help me

To determine the direction you would need to fly and the time it would take for the trip, we can break down the problem into two components: the groundspeed and the heading.

1. Groundspeed:
The groundspeed is the effective speed of the plane relative to the ground, taking into account the airspeed and the wind velocity. To calculate the groundspeed, we can use vector addition.

Let's represent the airspeed as A = 100 km/h (the speed of the plane) and the wind velocity as W = 45 km/h (the speed and direction of the wind).

The groundspeed (G) can be calculated as the vector sum of A and W:
G = A + W

Since A and W are in different directions (opposite sign), we need to subtract the velocity vectors to find the resultant:
G = A - W

Using this formula, we can determine the groundspeed:
G = 100 km/h - 45 km/h
G = 55 km/h

So, the groundspeed is 55 km/h.

2. Heading:
The heading is the direction in which you need to point the plane to follow the track to your destination. To calculate the heading, we can use trigonometry and the concept of angle of wind correction.

Let's denote the direction you need to fly as H, and the angle between your heading and the track as φ.

To find φ, we can use the formula:
tan(φ) = W / A

Plugging in the values:
tan(φ) = 45 km/h / 100 km/h

Using a calculator, we find:
φ ≈ 0.4636 radians

Now, to calculate the heading, we can simply subtract φ from 180° because the wind correction angle is the opposite direction of the wind:
H = 180° - φ

H ≈ 180° - 0.4636 ≈ 179.5364°

So, the direction you would have to fly (heading) is approximately 179.5364°.

3. Time calculation:
To calculate the time it would take for the trip, we need to divide the distance by the groundspeed:
Time = Distance / Groundspeed

Plugging in the values:
Time = 137.25 km / 55 km/h

Calculating this, we find:
Time ≈ 2.495 hours or approximately 2 hours and 30 minutes.

Therefore, you would have to fly at a heading of approximately 179.5364°, and the trip would take approximately 2 hours and 30 minutes.