A plane with airspeed of 500 mph is flying in the compass direction 35 degrees. Find the component form of the plane’s course.
North = y direction = 500 cos 35
East = x direction = 500 sin 35
To find the component form of the plane's course, we need to break down the velocity vector into its horizontal and vertical components.
Given:
Airspeed = 500 mph
Compass direction = 35 degrees
Step 1: Convert the compass direction to an angle measured counterclockwise from the positive x-axis.
Since the compass direction is given as 35 degrees, we subtract it from 90 degrees because the positive x-axis is at 90 degrees.
Angle = 90 degrees - 35 degrees = 55 degrees
Step 2: Find the horizontal and vertical components using trigonometry.
The horizontal component (x-axis) can be calculated using the cosine function:
Horizontal component = Cos(angle) * Airspeed
Horizontal component = Cos(55 degrees) * 500 mph
The vertical component (y-axis) can be calculated using the sine function:
Vertical component = Sin(angle) * Airspeed
Vertical component = Sin(55 degrees) * 500 mph
Step 3: Calculate the component values:
Horizontal component = 0.5736 * 500 mph = 286.8 mph (rounded to one decimal place)
Vertical component = 0.8192 * 500 mph = 409.6 mph (rounded to one decimal place)
Therefore, the component form of the plane's course is (286.8 mph, 409.6 mph).
To find the component form of the plane's course, we need to understand that the direction of the course is given by a compass direction angle, which is measured clockwise from due north.
In this case, the compass direction of the plane is 35 degrees. The airspeed of the plane is given as 500 mph.
To get the component form of the plane's course, we need to break down the velocity vector into its horizontal and vertical components.
First, we can find the horizontal component by multiplying the airspeed by the cosine of the compass direction angle.
Horizontal component = airspeed x cos(compass direction angle)
= 500 mph x cos(35 degrees)
Similarly, we can find the vertical component by multiplying the airspeed by the sine of the compass direction angle.
Vertical component = airspeed x sin(compass direction angle)
= 500 mph x sin(35 degrees)
Now, we have the horizontal and vertical components of the plane's course, which can be written in the component form as a vector:
Horizontal component, or the x-component: 500 mph x cos(35 degrees)
Vertical component, or the y-component: 500 mph x sin(35 degrees)
So, the component form of the plane's course is (500 mph x cos(35 degrees), 500 mph x sin(35 degrees)).