Question

Part A: Л1 (vector 1) /2 (work for vector 1) /1 (vector 2) 12 (work for vector 2)

Part B: 1 (added vectors)/1 (work shown)
Part C: /2 (speed) 1 (ref. andle) 1 (direction) /3 (work shown)
An airplane fies at 300 mph with a direction of 100 relative to the air. The plane experiences a wind that blows 40 mph with a direction of 60.
Part A: Write each of the vectors in linear form. Show all necessary calculations. (6 points)
Part B: Find the sum of the vectors. Showlnecessary calculations (2 points)
Part C: Find the true speed and direction of the airplane. Round the speed to the thousandths place and the direction to the nearest degree. Show all necessary calculations.

Answer 1

The question involves determining an airplane's true course and speed by using vector components, vector addition, and trigonometry to account for the effects of wind speed and direction.

Step-by-step explanation:

The student's question pertains to the calculation of vector addition in the context of an airplane's motion under the influence of the wind. The problem scenario addresses converting vector information into linear form, finding the resultant vector, and determining the true speed and direction of the airplane with given vectors for the airplane and wind.

Part A: Writing Vectors in Linear Form

To represent the airplane's motion and the wind vector in linear form, one would break down the vectors into their components using trigonometric functions. The airplane's vector is 300 mph at 100 degrees relative to the air, and the wind vector is 40 mph at 60 degrees. By finding the horizontal (x) and vertical (y) components, the vectors are translated into a more workable linear form, using sine and cosine functions.

Part B: Sum of Vectors

The sum of the two vectors is found by adding corresponding components of the two vectors – that is, adding the x-components together and the y-components together.

Part C: True Speed and Direction

The final speed and direction of the airplane (the resultant vector magnitude and direction) are found by computing the square root of the sum of the squares of the components for magnitude and using the arctan function to find the angle for direction, rounding to the nearest thousandths for speed and nearest degree for direction.