Find the component form of the following vectors. Round your answers to the tenth.
Magnitude of v = 50, direction angle θ = 50°
To find the component form of the vector with magnitude 50 and direction angle 50°, we can use the formulas:
x-component = magnitude * cosine(direction angle)
y-component = magnitude * sine(direction angle)
So, the x-component is:
x-component = 50 * cosine(50°) ≈ 50 * 0.6427876097 ≈ 32.139
And the y-component is:
y-component = 50 * sine(50°) ≈ 50 * 0.7660444431 ≈ 38.302
Therefore, the component form of the vector is approximately <32.139, 38.302>.
To find the component form of a vector given its magnitude and direction angle, we can use the following formulas:
v₁ = V * cos(θ)
v₂ = V * sin(θ)
Where V represents the magnitude of the vector and θ represents the direction angle.
Let's calculate the component form of the vector step-by-step:
Step 1: Given information
Magnitude of v = 50, direction angle θ = 50°
Step 2: Calculate the component form
Using the formulas above, we have:
v₁ = 50 * cos(50°)
v₁ = 50 * 0.6428
v₁ ≈ 32.14
v₂ = 50 * sin(50°)
v₂ = 50 * 0.7660
v₂ ≈ 38.30
Therefore, the component form of the vector is approximately (32.1, 38.3).