Question

Find the component form of the following vectors. Round your answers to the tenth.
Magnitude of v = 50, direction angle θ = 50°

Answer 1

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).