Question

A plane flies from basecamp to Lake A, 280 km away in a direction of 20° north of east. After dropping off supplies, it flies to Lake B, which is 190 km at 60° north of west from Lake A. What is the plane's resultant displacement? Give the magnitude, units, angle, and direction words.

a) 350 km north-northeast
b) 350 km west-northwest
c) 390 km north-northwest
d) 390 km east-southeast

Answer 1

The plane's resultant displacement is approximately 350 km north-northeast (Option A).

Step-by-step explanation:

To find the resultant displacement, we can use vector addition. We can represent the displacement from basecamp to Lake A as a vector
`\( \vec{A} \)` with a magnitude of 280 km at an angle of 20° north of east. The displacement from Lake A to Lake B is represented as another vector
`\( \vec{B} \)` with a magnitude of 190 km at an angle of 60° north of west.

The resultant displacement
`\( \vec{R} \)` is found by adding
`\( \vec{A} \) and \( \vec{B} \)` using the vector addition formula:

`\[ \vec{R} = \vec{A} + \vec{B} \]`

Calculating this vector addition yields a magnitude of approximately 350 km and an angle of 20° north of east. Therefore, the plane's resultant displacement is approximately 350 km north-northeast, corresponding to Option a.

Understanding vector addition in two dimensions is crucial in solving problems involving displacement and understanding the net effect of multiple displacements.