Velocity as a Vector: Plane Ground Velocity Calculation

In summary, the problem involves a light plane traveling at 175km/h on a heading of N8°E in a 40km/h wind from N80°E. To determine the plane's ground velocity, the components NS and EW must be calculated using trigonometry. The final answer is 167 km/h, N5°W.
  • #1
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Homework Statement



A light plane is traveling at 175km/h on a heading of N8°E in a 40km/h wind from N80°E. Determine the plane's ground velocity.

Homework Equations





The Attempt at a Solution



After I did all the graphing and trig. I came out with x^2 = 175^2 + 40^2 - 2(175)(40)cos108

which ends up being roughly 191.18, but the answer tells me its 167 km/h, N5°W

If anyone could help me out with this it would really be great, I am having a rough time with it.

Thanks for your time.
 
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  • #2
Break it up into components: NS, EW. The direction NS is y = 175 sin(82) - 40 sin(10), where + is N. The direction EW is x = 175cos(82)-40cos(10), where + is E. To get their length, calculate [tex]D = \sqrt{x^2+y^2} [/tex]. I'll leave the direction to you.
 
  • #3
Thanks a bunch! that helped tons!
 

FAQ: Velocity as a Vector: Plane Ground Velocity Calculation

What is velocity as a vector?

Velocity as a vector is a measure of the rate of change of an object's position, taking into account both its magnitude (speed) and direction. In other words, it describes how fast an object is moving and in what direction it is moving.

How is velocity as a vector different from speed?

Speed only measures the magnitude of an object's movement, while velocity as a vector takes into account both magnitude and direction. This means that two objects can have the same speed, but different velocities if they are moving in different directions.

How is plane ground velocity calculated?

Plane ground velocity is calculated by breaking down the velocity into its horizontal and vertical components, using trigonometry. The horizontal component is then used to calculate the distance traveled in a given time, while the vertical component is used to determine the object's altitude.

Why is it important to use velocity as a vector in scientific calculations?

Using velocity as a vector allows for more accurate and precise calculations, as it takes into account both magnitude and direction. This is especially important in fields such as physics and engineering, where precise measurements are crucial.

Can velocity as a vector change over time?

Yes, velocity as a vector can change over time if the speed or direction of an object changes. This is known as acceleration, which is the rate of change of an object's velocity. An object can also have a constant velocity if its speed and direction remain the same.

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