Kinematics -- flying a plane in the wind to a destination

• Philly215
In summary: I suggest you try using radians, or maybe if you insist on using degrees, use 5.74° and see how close you get. In summary, a plane is taking off with a constant speed of 730 km/h from an airport directly west of its destination. It needs to compensate for a wind blowing at 92 km/h in the direction of 45° S of E. To find the angle at which the plane must fly to compensate for the wind, we must use resultant triangles, components, and trigonometric functions (without using sin law). By drawing a diagram and adding the vectors of the plane's velocity and the wind's velocity, we can see that the resultant vector should point straight to the right (East
Philly215

Homework Statement

A plane is taking off from an airport directly west of the airport it wishes to touch down in. The plane in still air can travel with a constant speed of 730 km/h. If a wind is blowing constantly at 92 km/h [45° S of E], at what angle must the plane fly to compensate for the wind?

Homework Equations

Trig (sin, cos, tan) *no sin law*
V =d/t

The Attempt at a Solution

[/B]
730 km/h ÷ 92 km/h = 7.93 km/h
45/7.93= 5.67 ° [N of E]

* The answer for this question is 5.1° [N of E] and must be solved using resultant triangles, components and trig (no sin law). However, I am completely lost in solving this.

Last edited by a moderator:
Philly215 said:

Homework Statement

A plane is taking off from an airport directly west of the airport it wishes to touch down in. The plane in still air can travel with a constant speed of 730 km/h. If a wind is blowing constantly at 92 km/h [45° S of E], at what angle must the plane fly to compensate for the wind?

Homework Equations

Trig (sin, cos, tan) *no sin law*
V =d/t

The Attempt at a Solution

[/B]
730 km/h ÷ 92 km/h = 7.93 km/h
45/7.93= 5.67 ° [N of E]

* The answer for this question is 5.1° [N of E] and must be solved using resultant triangles, components and trig (no sin law). However, I am completely lost in solving this.
Welcome to the PF.

First, you should clarify what is meant by "[45° S of E]" -- does that mean the wind is coming from that direction, or blowing in that direction.

Next, draw a diagram showing the vectors of the plane's velocity (pointing left-to-right, angled either up or down), and the wind's velocity vector. When you place the vectors nose-to-tail (to add them), the resultant vector needs to point straight to the right (to the East).

Philly215 said:
730 km/h ÷ 92 km/h = 7.93 km/h
You divided km/h by km/h and got a result with units of km/h? Shouldn't the units cancel?
45/7.93= 5.67 ° [N of E]
What was your thinking on the above step, dividing 45° by 7.93?

Did you draw a sketch of how the vectors should add? What direction should the resultant have?

Edit: Ah! berkeman got there ahead of me!

Your mistake comes from assumption that x is proportional to sin(x) for degrees and such high value as 45°, try plugging the exact value of sin(45°). sin(x)~x for small angle values, but for x in radians.

1. How does the wind affect the flight of a plane?

The wind can significantly affect the flight of a plane. The direction and speed of the wind can cause the plane to drift off course and change its speed. Pilots must constantly adjust the plane's heading and speed to compensate for the wind in order to reach their destination.

2. What is the difference between airspeed and groundspeed?

Airspeed refers to the speed of the plane relative to the surrounding air, while groundspeed refers to the speed of the plane relative to the ground. Wind can affect the groundspeed of a plane, but not its airspeed. This means that even if a plane is flying at a constant airspeed, its groundspeed may vary due to the influence of the wind.

3. How does the pilot determine the correct heading and speed in order to reach their destination?

Pilots use a combination of tools and techniques to determine the correct heading and speed to reach their destination. They use instruments such as an airspeed indicator, a heading indicator, and a navigation system to constantly monitor their airspeed, direction, and position. They also use their training and experience to make adjustments based on weather conditions and other factors.

4. Can a plane fly directly into a headwind?

Yes, a plane can fly directly into a headwind. In fact, pilots often prefer to fly into a headwind as it can help slow down the plane's groundspeed, making it easier to land. However, flying into a strong headwind can also increase fuel consumption and extend the flight time.

5. How does the wind affect the takeoff and landing of a plane?

The wind can have a significant impact on the takeoff and landing of a plane. A strong headwind can help a plane take off at a shorter distance, while a tailwind can make the takeoff longer and more difficult. During landing, pilots must carefully adjust the plane's speed and angle of descent to compensate for the wind and ensure a safe landing.

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