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

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## 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.

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## 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].