I have tried this question over and over and not sure if the answer is 16 west or 190 south west please help. Airplane One flies due east at 250 km/h relative to the ground. At the same time, Airplane Two flies 325 km/h, 35° north of east relative to the ground. What is the velocity of Airplane One relative to Airplane Two?
To find the velocity of Airplane One relative to Airplane Two, we need to combine their velocities using vector addition.
First, let's break down the velocities of each airplane into their components.
Airplane One is flying due east, so its velocity can be broken down into two components: one along the north-south axis (y-axis) and one along the east-west axis (x-axis). Since it is flying due east, there is no north-south component, so the y-component is 0 km/h. The x-component is 250 km/h.
Airplane Two is flying 35° north of east. To break down its velocity into components, we can use trigonometry. The angle between the direction of travel and the north-south axis is 90° - 35° = 55°. The velocity component along the north-south axis (y-axis) can be calculated as 325 km/h * sin(55°), and the velocity component along the east-west axis (x-axis) can be calculated as 325 km/h * cos(55°).
Now, we can add the corresponding components of Airplane One and Airplane Two to find the velocity of Airplane One relative to Airplane Two.
The y-component of Airplane One's velocity is 0 km/h, and the y-component of Airplane Two's velocity is 325 km/h * sin(55°).
The x-component of Airplane One's velocity is 250 km/h, and the x-component of Airplane Two's velocity is 325 km/h * cos(55°).
To find the net velocity, we add the corresponding components:
Net y-component = 0 km/h + 325 km/h * sin(55°)
Net x-component = 250 km/h + 325 km/h * cos(55°)
Using trigonometry to evaluate sin(55°) and cos(55°), we can calculate the magnitudes of the components, and finally use the Pythagorean theorem to find the net velocity:
Magnitude of the net velocity = sqrt((Net x-component)^2 + (Net y-component)^2)
By using this process, you can calculate the velocity of Airplane One relative to Airplane Two.