Position vector r has magnitude of 14.8m and direction angle 240 degrees.
1. Find it's components, enter x and y components of the vector
2. Find the components of the vector
-2r, enter x and y components of the vector
3. Find the magnitude of the vector -2r.
To find the components of the position vector r given its magnitude and direction angle, we can use trigonometry.
1. Finding the components of vector r:
The magnitude of vector r is given as 14.8m, and the direction angle is 240 degrees.
Let's call the x-component of vector r as Rx and the y-component as Ry.
To find Rx, we can use cosine:
Rx = magnitude * cos(direction angle)
Rx = 14.8m * cos(240 degrees)
To find Ry, we can use sine:
Ry = magnitude * sin(direction angle)
Ry = 14.8m * sin(240 degrees)
Calculating these values will give us the x and y components of vector r.
2. Finding the components of vector -2r:
To find the components of -2r, we simply multiply the x and y components of vector r by -2.
So, the x-component of -2r is -2 * Rx, and the y-component of -2r is -2 * Ry.
3. Finding the magnitude of vector -2r:
The magnitude of a vector is calculated using the Pythagorean theorem:
Magnitude = sqrt((Rx)^2 + (Ry)^2)
For vector -2r, we calculate the magnitude in the same way but using the x and y components we found in step 2:
Magnitude of -2r = sqrt((x-component of -2r)^2 + (y-component of -2r)^2)
By finding the square root of the sum of the squares of the x and y components, we can determine the magnitude of vector -2r.
To find the components of the vector r, we can use trigonometry.
1. The magnitude of the vector r is 14.8m, and the direction angle is 240 degrees.
The x-component can be calculated as:
x = magnitude * cos(direction angle) = 14.8m * cos(240 degrees) ≈ -7.4m
The y-component can be calculated as:
y = magnitude * sin(direction angle) = 14.8m * sin(240 degrees) ≈ -12.8m
Therefore, the components of the vector r are approximately x = -7.4m and y = -12.8m.
2. To find the components of the vector -2r, we multiply the components of r by -2.
The x-component of -2r is:
-2 * x = -2 * -7.4m = 14.8m
The y-component of -2r is:
-2 * y = -2 * -12.8m = 25.6m
Therefore, the components of -2r are x = 14.8m and y = 25.6m.
3. To find the magnitude of the vector -2r, we can use the Pythagorean theorem:
magnitude = sqrt((x^2) + (y^2)) = sqrt((14.8m^2) + (25.6m^2))
≈ sqrt(218.24m^2)
≈ 14.77m
Therefore, the magnitude of the vector -2r is approximately 14.77m.