Position vector r⃗ has magnitude of 19.4m and direction angle 235 degrees
What are the x and y components? (x,y)
Find the components of the vector −2r⃗ and the magnitude of the vector?
Find components of vector -2r
x = 19.4 cos 235°
y = 19.4 sin 235°
multiply by -2 to get the x,y of -2r.
multiply 19.4 by 2 to get the magnitude
To find the x and y components of a vector given the magnitude and direction angle, follow these steps:
1. Convert the direction angle from degrees to radians by multiplying it by π/180.
- In this case, the direction angle is 235 degrees:
235 degrees × (π/180) = 4.101 radians
2. Use the magnitude to find the x and y components using trigonometric functions.
- The x-component, rx, is given by: rx = magnitude × cos(direction angle)
- The y-component, ry, is given by: ry = magnitude × sin(direction angle)
- Plug in the values:
rx = 19.4m × cos(4.101 radians)
ry = 19.4m × sin(4.101 radians)
3. Calculate the components:
- rx = 19.4m × cos(4.101 radians) ≈ -17.142 m
- ry = 19.4m × sin(4.101 radians) ≈ 2.054 m
Therefore, the x and y components of vector r⃗ are approximately (rx, ry) = (-17.142 m, 2.054 m).
To find the components of the vector -2r⃗, we simply multiply the x and y components of r⃗ by -2.
-2r⃗ = (-2rx, -2ry) = (-2(-17.142 m), -2(2.054 m)) = (34.284 m, -4.108 m)
The magnitude of the vector -2r⃗ can be found using the Pythagorean theorem:
Magnitude of -2r⃗ = √((-2rx)^2 + (-2ry)^2)
= √((34.284 m)^2 + (-4.108 m)^2)
≈ 34.76 m
Therefore, the components of the vector -2r⃗ are (34.284 m, -4.108 m) and its magnitude is approximately 34.76 m.