Calculate Plane Velocity Relative to Ground in Different Directions

In summary, the conversation discusses the determination of the velocity of a small plane relative to the ground, given its airspeed of 200 km/h and wind speed of 50.0 km/h [E]. The directions considered are East, West, North, and North 40° East, with the last one requiring the use of the head to tail method for vector addition. The conversation also mentions the use of the Pythagorean method, which is only applicable for vectors forming a right angle.
  • #1
Quantum Mind
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0

Homework Statement



The airspeed of a small plane is 200 km/h. The wind speed is 50.0 km/h [E]. Determine the velocity of the plane
relative to the ground if the pilot keeps the plane pointing in each of the following directions.
a) East (250 km/h [E] )
b) West (150 km/h [W] )
c) North (206 km/h [N14.0°E])
d) North 40° East (2.4e2 km/h [E41°N] )

Homework Equations


Sin Theta = opp/hyp where Theta = 40 deg, Hyp=200.

The Attempt at a Solution



The first three are basic. For the fourth obviously, a simple resolution of vectors won't do. If I do, I get 128, while the answer is 240. What am I doing wrong?

Sorry to sound so stupid, I am a novice at physics. :confused:
 
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  • #2
The Pythagorean method is only useful for adding vectors that form a right angle. What other methods of vector addition have you covered?
 
  • #3
OK, I got it. Thanks. I have to use the head to tail method.
 

What is the formula for calculating the plane's velocity relative to ground in different directions?

The formula for calculating the plane's velocity relative to ground in different directions is V = √(Vx^2 + Vy^2), where V is the total velocity, Vx is the velocity in the x-direction, and Vy is the velocity in the y-direction.

What is the difference between ground speed and airspeed for a plane?

Ground speed is the speed at which the plane is moving relative to the surface of the Earth, while airspeed is the speed at which the plane is moving relative to the air around it. Ground speed takes into account factors such as wind and airspeed does not.

How does the direction of wind affect the plane's velocity relative to ground?

The direction of wind can affect the plane's velocity relative to ground by either increasing or decreasing its speed depending on whether the wind is in the same direction or opposite direction as the plane's motion. The wind's direction also affects the direction in which the plane will travel.

Why is it important to calculate the plane's velocity relative to ground in different directions?

It is important to calculate the plane's velocity relative to ground in different directions in order to accurately navigate and control the plane's movement. This information is crucial for pilots to make informed decisions and maintain the safety of the flight.

What factors can affect the accuracy of calculating the plane's velocity relative to ground?

The accuracy of calculating the plane's velocity relative to ground can be affected by factors such as wind speed and direction, air density, altitude, and the precision of the instruments used to measure the velocity. Human error can also play a role in the accuracy of the calculation.

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