A vector representing 170 N is oriented at 59◦ with the horizontal.
What is the magnitude of its horizontal component?
Answer in units of N.
What is the magnitude of its vertical compo- nent?
Answer in units of N.
To find the horizontal component of the vector, we need to find the magnitude of the vector multiplied by the cosine of the angle it makes with the horizontal.
1. First, convert the angle from degrees to radians. We can do this by multiplying the angle by π/180:
angle_in_radians = 59° × π/180 = 1.0297 rad (rounded to four decimal places)
2. Now, use the formula for finding the horizontal component of a vector:
horizontal_component = magnitude × cos(angle_in_radians)
horizontal_component = 170 N × cos(1.0297 rad) ≈ 170 N × 0.5362 ≈ 91.17 N
Therefore, the magnitude of the vector's horizontal component is approximately 91.17 N.
To find the vertical component of the vector, we need to find the magnitude of the vector multiplied by the sine of the angle it makes with the horizontal.
3. Use the formula for finding the vertical component of a vector:
vertical_component = magnitude × sin(angle_in_radians)
vertical_component = 170 N × sin(1.0297 rad) ≈ 170 N × 0.8443 ≈ 143.47 N
Therefore, the magnitude of the vector's vertical component is approximately 143.47 N.