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 a vector, we need to find the horizontal and vertical components of the vector.
The horizontal component (v_x) can be found by multiplying the magnitude of the vector (50) by the cosine of the direction angle (50°).
The vertical component (v_y) can be found by multiplying the magnitude of the vector (50) by the sine of the direction angle (50°).
Using these formulas, we can calculate the components of the vector as follows:
v_x = 50 * cos(50°)
v_x ≈ 50 * 0.6428
v_x ≈ 32.14
v_y = 50 * sin(50°)
v_y ≈ 50 * 0.7660
v_y ≈ 38.30
Therefore, the component form of the vector is (32.1, 38.3) (rounded to the nearest tenth).
To find the component form of the vector, we need to find the horizontal and vertical components.
The horizontal component (x-component) is given by:
𝑥 = 𝑉 ∙ 𝑐𝑜𝑠(𝜃)
where 𝑉 is the magnitude of the vector and 𝜃 is the direction angle.
Substituting the given values, we get:
𝑥 = 50 ∙ 𝑐𝑜𝑠(50°)
Using a calculator, we find:
𝑥 ≈ 38.397
The vertical component (y-component) is given by:
𝑦 = 𝑉 ∙ 𝑠𝑖𝑛(𝜃)
where 𝑉 is the magnitude of the vector and 𝜃 is the direction angle.
Substituting the given values, we get:
𝑦 = 50 ∙ 𝑠𝑖𝑛(50°)
Using a calculator, we find:
𝑦 ≈ 38.397
Therefore, the component form of the vector is (38.4, 38.4).