Relative velocity - plane flying

In summary, the plane needs to head 19 degrees west of north in order to fly due north relative to the ground. The speed of the plane relative to the ground is 237 km/h. The correct answer for the direction is 16 degrees west of north and for the speed is 280 km/h. It seems that there may have been an error in the calculations or equations used.
  • #1

Homework Statement

A plane flies at an airspeed of 250 km/h. A wind is blowing at 80 km/h toward the direction 60* east of north.
a) In what direction should the plane head in order to fly due north relative to the ground?
b) What is the speed of the plane relative to the ground?

Homework Equations

it's too messy to write the equations down, but I used position vector of plane relative to the ground and the Pythagorean theorem

The Attempt at a Solution

for a:

sin x = 30/250 = 8/25

sin inverse 8/25 = 19 degrees

so my answer to a is 19 degrees west of north. the back of the book says the answer is 16 degrees west of north. What did I do wrong?

for b:

V (plane to ground) = squar root of (250^2 + 80^2) = 237 km/h

the answer in the back of the book is 280 km/s so even even I converted to seconds my answer would be way off. Again, I don't know what I did wrong...
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  • #2

1. What is relative velocity?

Relative velocity is the velocity of an object with respect to a different object or frame of reference. It is the difference between the velocities of the two objects.

2. How does relative velocity apply to planes flying?

In the context of planes flying, relative velocity refers to the velocity of the plane relative to the ground. This can be affected by factors such as the speed and direction of the wind, and can impact the plane's speed and travel time.

3. Can relative velocity be negative?

Yes, relative velocity can be negative. This occurs when the two objects are moving in opposite directions, resulting in a negative difference between their velocities.

4. How is relative velocity calculated?

Relative velocity is calculated by subtracting the velocity of one object from the velocity of the other object. This can be represented by the equation vrel = v1 - v2, where vrel is the relative velocity, v1 is the velocity of the first object, and v2 is the velocity of the second object.

5. Why is understanding relative velocity important for flying?

Understanding relative velocity is important for flying because it allows pilots to accurately calculate the plane's speed and travel time based on factors such as wind speed and direction. It also helps with navigation and avoiding collisions with other objects in the air.

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