Question

The problem asks to find the resultant force from the given diagram. However, the question itself is incomplete as it does not explicitly state what needs to be calculated (e.g., resultant of all forces, or a subset of forces) and the magnitudes of two of the forces are missing. Assuming the task is to find the resultant of the forces whose magnitudes are provided (Force T and Force S), we proceed as follows:

• A. 3î + 5ĵ
• B. 3î + 15ĵ

Answer 1

No Option Found

Answer 2

1. Identify forces with given magnitudes (T and S).

2. Determine the angle of each force with respect to the positive x-axis.

   • For T (15N, 2nd quadrant, 60° with negative x-axis): Angle = $180^\circ - 60^\circ = 120^\circ$.
   • For S (15N, 3rd quadrant, 45° with negative x-axis): Angle = $180^\circ + 45^\circ = 225^\circ$.

3. Calculate x and y components for each force:

   • $\vec{T} = (15 \cos 120^\circ)\hat{i} + (15 \sin 120^\circ)\hat{j} = -7.5\hat{i} + 7.5\sqrt{3}\hat{j}$
   • $\vec{S} = (15 \cos 225^\circ)\hat{i} + (15 \sin 225^\circ)\hat{j} = -7.5\sqrt{2}\hat{i} - 7.5\sqrt{2}\hat{j}$

4. Sum the components to find the resultant vector:

   • $\vec{R} = (-7.5 - 7.5\sqrt{2})\hat{i} + (7.5\sqrt{3} - 7.5\sqrt{2})\hat{j}$
   • $\vec{R} \approx -18.11\hat{i} + 2.39\hat{j}$

5. Compare the calculated resultant with the given options. The calculated resultant does not match any of the options provided, especially due to the negative x-component. The question is incomplete or contains errors.