How Do You Calculate the Speed of a Plane with Respect to the Ground?

[aruji73]

You are traveling on an airplane. The velocity of the plane with respect to the air is 120.0 m/s due east. The velocity of the air with respect to the ground is 43.0 m/s at an angle of 30° west of due north.

1.What is the speed of the plane with respect to the ground?

I got 82.76 by doing 120-43(cos30)

but apparently it was wrong the feedback i got was It looks like you incorrectly calculated the planes velocity with respect to the ground in the east direction. Be careful when you calculate the east-west component of the wind's velocity. Also don't forget to include the winds north-south component to get the total speed of the plane with respect to the ground.

 

[Simon Bridge]

Very good - did you have a question?

 

[aruji73]

ya that's apparently wrong how do I get the correct solution

 

[Simon Bridge]

Well, your answer does not have a direction or any units and you did not supply any reasoning.

The advise you have is that you made a mistake in your reasoning.
Go back over it again and consider - what does the wind do with the plane?
Perhaps if you drew a picture
- which direction is the "43cos(30)" part pointing in?
- which direction is the "120" part pointing in

 

[Nickie]

I would like to clarify that the speed of an object is the magnitude of its velocity. In this case, we are dealing with relative motion, which means we are considering the motion of the plane with respect to both the air and the ground. Therefore, the total speed of the plane with respect to the ground would be calculated by taking into account both the east-west and north-south components of its velocity.

To calculate the total speed, we can use the Pythagorean theorem, which states that the hypotenuse of a right triangle (in this case, the total velocity of the plane) is equal to the square root of the sum of the squares of its two perpendicular sides (in this case, the east-west and north-south components).

Using this formula, we can calculate the total speed of the plane with respect to the ground as:

Total speed = √[(120 m/s)^2 + (43 m/s)^2] = √(14400 m^2/s^2 + 1849 m^2/s^2) = √16249 m^2/s^2 = 127.38 m/s

Therefore, the speed of the plane with respect to the ground is approximately 127.38 m/s, which is greater than 82.76 m/s that was calculated earlier. This is because we need to consider both the east-west and north-south components of the plane's velocity to get the total speed with respect to the ground. I hope this clarification helps in understanding the concept of relative and circular motion better.