A jet is flying through wind blowing 55mi/h at a bearing (clockwise from north) of 35°. The jet is flying with a speed of 550 mi/h at a bearing of 65°. Find the resultant of the planes velocity vector and the winds velocity vector. Also find its magnitude and direction. This represents the true velocity of the plane (neglecting resistance).
All angles are measured CCW from +x-axis.
Vr = 55mi/h[55o] + 550mi/h[25o] =
31.5+45.1i + 498+232i = 530 + 277i = 598mi/h[27.6o]
To find the resultant of the plane's velocity vector and the wind's velocity vector, we can use vector addition.
Step 1: Resolve the velocities into their horizontal and vertical components.
The wind's velocity has a magnitude of 55 mi/h and a bearing of 35° clockwise from north.
The plane's velocity has a magnitude of 550 mi/h and a bearing of 65° clockwise from north.
For the wind's velocity:
Horizontal component = 55 mi/h * cos(35°)
Vertical component = 55 mi/h * sin(35°)
For the plane's velocity:
Horizontal component = 550 mi/h * cos(65°)
Vertical component = 550 mi/h * sin(65°)
Step 2: Add the horizontal components and the vertical components separately.
Resultant horizontal component = wind's horizontal component + plane's horizontal component
Resultant vertical component = wind's vertical component + plane's vertical component
Step 3: Calculate the magnitude and direction of the resultant vector using the horizontal and vertical components.
Magnitude of the resultant vector = sqrt((resultant horizontal component)^2 + (resultant vertical component)^2)
Direction of the resultant vector = atan2(resultant vertical component, resultant horizontal component)
By following these steps, we can find the resultant velocity vector of the plane and the wind, as well as its magnitude and direction.