Kyle wishes to fly to a point 450 km due south in 3 hours. A wind is blowing from the west at 50 km/hr. Compute the proper heading and speed that Kyle must choose in order to reach his destination on time.

His southerly velocity must be 450km/3hrs.

Now draw the vectors. You have a resultant, Due South, of 150km/hr, a component due E at 50km/hr, Let theta be the angle of his flying, so on my diagram, I see tan Theta= 150/50=3
or Theta= 71.6deg S of W, or a heading of
270-71.6=198.4 deg
check that.
His speed? 50/speed=cos71.4, solve for speed
Double check me on all this.

To compute the proper heading and speed that Kyle must choose to reach his destination on time, we need to take into account the wind's effect on his flight.

1. First, we'll calculate the component of the wind that is acting against Kyle's intended path.
- The wind is blowing from the west at a speed of 50 km/hr.
- Since Kyle wants to fly south, we need to find the westward component of the wind.
- This can be calculated using trigonometry: west speed = wind speed * cos(theta), where theta is the angle between the wind direction and Kyle's intended path.
- Since the wind is blowing from the west, the angle theta is 90 degrees.
- So, west speed = 50 km/hr * cos(90 degrees) = 0 km/hr.

2. Next, we'll calculate the ground speed and heading that Kyle needs to choose in order to counteract the westward component of the wind and maintain a southward track.
- Ground speed is the speed at which Kyle needs to fly relative to the ground.
- Ground speed = required speed + wind speed.
- Since Kyle wishes to fly at a speed of 450 km/h southward, the required speed is 450 km/h.
- Using the calculated west speed of 0 km/hr, the ground speed becomes 450 km/hr + 0 km/hr = 450 km/hr.
- The heading is the direction in which Kyle should fly relative to the true north, taking into account the wind.
- Since Kyle wants to fly due south, the heading will be the same as the true south direction, which is 180 degrees.

Therefore, Kyle must choose a heading of 180 degrees and a ground speed of 450 km/hr in order to reach his destination on time.

To determine the proper heading and speed that Kyle must choose in order to reach his destination on time, we need to consider the effect of the wind on his flight.

First, let's break down the problem into components:

1. Distance: Kyle wishes to fly 450 km south.
2. Time: He has 3 hours to reach his destination.
3. Wind: A wind is blowing from the west at 50 km/hr.

Now, let's find the ground speed and heading that Kyle must choose:

1. Ground Speed: The ground speed is the speed at which Kyle will actually be flying, considering the wind's effect. To calculate the ground speed, we need to subtract the wind's speed from the true airspeed.

Ground Speed = True Airspeed - Wind Speed

In this case, the true airspeed is the speed at which Kyle wants to fly, and the wind speed is 50 km/hr. Let's denote the ground speed as G.

G = True Airspeed - 50

2. Heading: The heading is the direction in which Kyle should navigate. To compute the heading, we need to take into account the effect of the wind. Since the wind is coming from the west and Kyle wants to fly due south, the heading should be adjusted to compensate for the wind.

Let's denote the heading as H.

To find the heading, we can use the concept of vector addition. We can break down Kyle's desired direction (south) into north and east components. The north component (N) will be 0 km/hr since he wants to go south, and the east component (E) will be the wind's speed (50 km/hr) since the wind is coming from the west.

So, the heading (H) can be calculated using the inverse tangent formula:

H = arctan(E/N)

In this case, E = 50 km/hr and N = 0 km/hr.

Now, let's calculate the values:

1. Ground Speed (G) = True Airspeed - Wind Speed
G = True Airspeed - 50 km/hr

2. Heading (H) = arctan(E/N)
E = 50 km/hr
N = 0 km/hr

Please provide the true airspeed value, and I can help you calculate the ground speed and heading that Kyle must choose.