A person walks $4$ km east and then $3$ km north. What is the magnitude of the resultant displacement from the starting point?

• A. $\sqrt{4^2+3^2}$ km
• B. $7$ km
• C. $5$ km
• D. $1$ km

Answer: (A)

Verified step by step guidance

1. Identify the two displacement vectors: one is 4 km east and the other is 3 km north. These two displacements are perpendicular to each other.
2. Represent the displacements as vectors along the x-axis (east) and y-axis (north). So, the displacement vector components are \$4\ \text{km}\( in the x-direction and \)3\ \text{km}$ in the y-direction.
3. To find the magnitude of the resultant displacement, use the Pythagorean theorem because the two displacements form a right-angled triangle.
4. Write the formula for the magnitude of the resultant displacement \(R\) as: \(R = \sqrt{(4)^2 + (3)^2}\)
5. Calculate the square of each component, sum them, and then take the square root to find the magnitude of the resultant displacement.