# A helicopter flies 65km [N32°E] then 42km[E 21°] determine the total displacement of the helicopter.

## my answer

## I agree. I used the law of cosines.

## To determine the total displacement of the helicopter, we can break down the two displacements into their horizontal and vertical components.

1. First, let's analyze the displacement of 65km [N32°E]:

- The direction N32°E means the displacement is 32° east of north (clockwise from north direction).

- We can split this displacement into its horizontal (east-west) and vertical (north-south) components using trigonometry:

- Horizontal component = 65km * cos(32°)

- Vertical component = 65km * sin(32°)

2. Next, let's analyze the displacement of 42km [E21°]:

- The direction E21° means the displacement is 21° east of east (counterclockwise from east direction).

- Since this displacement is purely horizontal, it only affects the east-west component.

3. Now, let's calculate the horizontal and vertical components for each displacement:

- Displacement 1:

- Horizontal component = 65km * cos(32°)

- Vertical component = 65km * sin(32°)

- Displacement 2:

- Horizontal component = 42km * cos(21°)

- Vertical component = 0 (since it is a purely horizontal displacement)

4. Finally, to determine the total displacement, we can add the horizontal and vertical components separately:

- Total horizontal displacement = Horizontal component of Displacement 1 + Horizontal component of Displacement 2

- Total vertical displacement = Vertical component of Displacement 1 + Vertical component of Displacement 2

By calculating the total horizontal and vertical displacements, you can find the magnitude and direction of the total displacement vector using the Pythagorean theorem and trigonometry.

## All angles are measured CCW from +x-axis.

Disp. = 65km[58o] + 42km[21o].

(65*Cos58+65*sin58) + (42*Cos21+42*sin21 =

(34.44+55.12i) + (39.21+15.05i) =

73.65 + 70.17i = 101.7km[43.6o].