Question

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

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

\vec{f}_x = ? n

Explanation:

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

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

$$ F_{1x} = F_1 \cos(\theta_1) = 115 \cos(75.0^\circ) \approx 29.764\text{ N} $$

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

$$ F_{2x} = F_2 \cos(\theta_2) = 213 \cos(295^\circ) \approx 89.998\text{ N} $$

Step 3: Sum the x-components

$$ F_x = F_{1x} + F_{2x} = 29.764 + 89.998 \approx 119.76\text{ N} $$

Rounding to three significant figures:

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

Answer:

120