Given information:
- Magnitude of one force: p
- Magnitude of the other force: q
- Angle between the forces: 60 degrees
- Resultant of the forces: √13q

To find:
The value of p/q

Explanation:

Step 1: Decompose the forces into their components
Let's consider the two forces as vectors A and B. To find the resultant, we need to decompose these vectors into their components.

The x-component of vector A can be found using the equation:
A_x = A * cos(60°) = p * cos(60°) = 0.5p

The y-component of vector A can be found using the equation:
A_y = A * sin(60°) = p * sin(60°) = √3/2 * p

Similarly, the x-component of vector B can be found using the equation:
B_x = B * cos(60°) = q * cos(60°) = 0.5q

The y-component of vector B can be found using the equation:
B_y = B * sin(60°) = q * sin(60°) = √3/2 * q

Step 2: Add the components of the forces
To find the resultant, we add the x-components and y-components separately.

The x-component of the resultant (R_x) can be found by adding the x-components of A and B:
R_x = A_x + B_x = 0.5p + 0.5q = 0.5(p + q)

The y-component of the resultant (R_y) can be found by adding the y-components of A and B:
R_y = A_y + B_y = √3/2 * p + √3/2 * q = √3/2(p + q)

Step 3: Find the magnitude of the resultant
The magnitude of the resultant (R) can be found using the Pythagorean theorem:
R^2 = R_x^2 + R_y^2

Substituting the values of R_x and R_y:
R^2 = (0.5(p + q))^2 + (√3/2(p + q))^2
R^2 = (1/4)(p + q)^2 + (3/4)(p + q)^2
R^2 = (4/4)(p + q)^2
R^2 = (p + q)^2

Taking the square root of both sides:
R = √(p + q)^2
R = p + q

Step 4: Equate the magnitude of the resultant to √13q
p + q = √13q

Step 5: Solve for p/q
p + q = √13q
p = √13q - q
p = (√13 - 1)q

Therefore, p/q = (√13 - 1)/1 = √13 - 1