Final answer:
To resolve a vector into horizontal and vertical components, trigonometric functions are used. For a 60N vector at a 30-degree angle from the horizontal, the components are determined using cosine and sine, resulting in horizontal and vertical components of approximately 52N and 30N, respectively.
Step-by-step explanation:
Vector Components in Physics
To resolve a vector into its components at an angle from the horizontal, we use trigonometric functions. Given a vector of 60N at a 30-degree angle from the horizontal, we start by drawing the vector. According to the scale provided, this vector would be represented by an arrow that is 3 cm long, pointing to the right, since we define the positive direction as to the right.
Now, to find the horizontal (x) and vertical (y) components of this vector, we use the equations:
Horizontal Component (F1x) = F1 cos(θ) = 60N cos(30°)
Vertical Component (F1y) = F1 sin(θ) = 60N sin(30°)
After calculating, the horizontal component (F1x) will be approximately 52N, and the vertical component (F1y) will be 30N. It's important to draw the horizontal and vertical components starting at the tail of F1 and at right angles to each other, forming a right-angle triangle with F1 as the hypotenuse.
We continue by adding additional vectors as described. For example, the next vector F2 is 90N in the same direction as F1 and should be represented by an arrow 4.5 cm long to the right. F3 is 100N in the opposite direction and should be drawn 5 cm long to the left, possibly as a separate vector for clarity to avoid a messy diagram.
To sum up forces in one dimension, we simply add or subtract the magnitudes depending on their directions, treating the right direction as positive and left as negative.