Two forces, 30 N and 40 N, act at right angles to each other. Using a scale of 1 cm = 5 N, find the magnitude and direction of their resultant force using a scale drawing.

We have two forces acting at a right angle:
$F_1 = 30 \text{ N}$
$F_2 = 40 \text{ N}$
The given scale for drawing is $1 \text{ cm} = 5 \text{ N}$.

To represent $F_1 = 30 \text{ N}$ on the drawing:

To represent $F_2 = 40 \text{ N}$ on the drawing:

• Draw the first force vector ($F_1$) as a line segment $6 \text{ cm}$ long. Let's assume it acts horizontally.
• From the head (end) of the first vector, draw the second force vector ($F_2$) as a line segment $8 \text{ cm}$ long, perpendicular to the first vector (since they act at a right angle).
• The resultant force vector ($R$) is drawn from the tail (start) of the first vector to the head of the second vector.
• Measure the length of this resultant vector ($R$) with a ruler. Convert this length back to Newtons using the scale ($1 \text{ cm} = 5 \text{ N}$).
• Measure the angle ($\theta$) the resultant vector makes with the first force vector using a protractor. This angle represents the direction.

Since the forces are at a right angle, we can use the Pythagorean theorem:

Substitute the force values:

The direction $\theta$ can be found using the tangent function, where $\theta$ is the angle the resultant makes with the $30 \text{ N}$ force:

The magnitude of the resultant force is $\boxed{\text{50 N}}$.
The direction of the resultant force is $\boxed{\text{53.13}^\circ \text{ from the 30 N force}}$.