Airplane one flies due to East at 250Km/h relative to the ground. At the same time, Airplane two flies 325Km/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 break down each airplane's velocity into its horizontal and vertical components. Let's start with Airplane one:
Airplane one is flying due East at 250 km/h relative to the ground, which means its horizontal velocity component is 250 km/h. Since it is flying due East, it does not have any vertical velocity component.
Now let's analyze Airplane two's velocity:
Airplane two is flying 325 km/h, 35° north of East. To find the horizontal and vertical components of its velocity, we can use trigonometry.
The horizontal component of Airplane two's velocity can be found by multiplying its total velocity (325 km/h) by the cosine of the angle (35°) north of East.
Horizontal component of Airplane two's velocity = 325 km/h * cos(35°)
Horizontal component of Airplane two's velocity = 325 km/h * 0.8192
Horizontal component of Airplane two's velocity ≈ 266 km/h
The vertical component of Airplane two's velocity can be found by multiplying its total velocity (325 km/h) by the sine of the angle (35°) north of East.
Vertical component of Airplane two's velocity = 325 km/h * sin(35°)
Vertical component of Airplane two's velocity = 325 km/h * 0.5736
Vertical component of Airplane two's velocity ≈ 186 km/h
Now, to find the velocity of Airplane one relative to Airplane two, we subtract the horizontal and vertical components of Airplane two from Airplane one's velocity.
Horizontal velocity of Airplane one relative to Airplane two = 250 km/h - 266 km/h ≈ -16 km/h
Vertical velocity of Airplane one relative to Airplane two = 0 km/h - 186 km/h ≈ -186 km/h
Therefore, the velocity of Airplane one relative to Airplane two is approximately -16 km/h horizontally and -186 km/h vertically. The negative sign indicates that Airplane one is moving in the opposite direction of Airplane two.