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].