Question

a block is pulled by two horizontal forces. the first force is (115\text{ n}) at an angle of (75.0^circ) and the second is (213\text{ n}) at an angle of (295^circ).

what is the x-component of the total force acting on the block?

(vec{f}_x = ? \text{ n})

Explanation:

⚡ Using what you learned: Vectors in Plane and Space (components, magnitude, direction)

Step 1: Find the x-component of the first force

$$ F_{1x} = 115 \cos(75.0^\circ) \approx 29.764\text{ N} $$

Step 2: Find the x-component of the second force

$$ F_{2x} = 213 \cos(295^\circ) \approx 89.985\text{ N} $$

Step 3: Sum the x-components

$$ F_x = F_{1x} + F_{2x} = 29.764 + 89.985 \approx 119.75\text{ N} $$

Rounding to three significant figures:

$$ F_x \approx 120\text{ N} $$

Answer:

120