r vector=(340m, 39 degrees below positive x-axis) What is rx and ry? I have no idea how to do or approach this problem, anyone please help and explain how to do this? Thank you!
To find the rectangular components of the given vector, we can use trigonometry. Here's how you can do it:
Step 1: Draw a coordinate system with positive x-axis pointing to the right and positive y-axis pointing upward.
Step 2: Start at the origin (0,0) and move 340 meters in the direction of 39 degrees below the positive x-axis.
Step 3: To find the x-component, we need to find the horizontal displacement in the x-direction. This can be found using the formula: rx = r * cos(theta), where r is the magnitude of the vector and theta is the angle measured counterclockwise from the positive x-axis.
In this case, r = 340 meters and theta = 39 degrees below the positive x-axis. Convert the angle to radians (since trigonometric functions in most calculators require angles to be in radians):
theta_radians = 39 degrees * (pi/180) = 0.6807 radians
Now, calculate rx = 340 * cos(0.6807) = 340 * 0.764 = 259.76 meters
So the x-component (rx) of the vector is 259.76 meters.
Step 4: To find the y-component, we need to find the vertical displacement in the y-direction. This can be found using the formula: ry = r * sin(theta), where r is the magnitude of the vector and theta is the angle measured counterclockwise from the positive x-axis.
In this case, r = 340 meters and theta = 39 degrees below the positive x-axis. Convert the angle to radians:
theta_radians = 39 degrees * (pi/180) = 0.6807 radians
Now, calculate ry = 340 * sin(0.6807) = 340 * 0.645 = 219.3 meters
So the y-component (ry) of the vector is 219.3 meters.
Therefore, the rectangular components of the vector are: rx = 259.76 meters and ry = 219.3 meters.