Question

A hiker walks 10.27 m, N, and 6.28 m, E. What is the magnitude of his resultant displacement? a) 10.27 m b) 6.28 m c) 16.55 m d) 2.99 m

Answer 1

The magnitude of the resultant displacement is 12.04 m. None of the given options is answer.

Step-by-step explanation:

The hiker's displacement can be represented by a vector with components in the x (east) and y (north) directions. The x-component is 10.27 m and the y-component is 6.28 m. The magnitude of the resultant displacement is the length of this vector.

Using the Pythagorean theorem, we can calculate the magnitude of the resultant displacement as follows:

|resultant_displacement| = √(x² + y²)

where:

|resultant_displacement| is the magnitude of the resultant displacement

x is the x-component of the displacement

y is the y-component of the displacement

Plugging in the values we know, we get:

|resultant_displacement| = √(10.27² + 6.28²) = 12.04 m

Therefore, the magnitude of the resultant displacement is 12.04 m

None of the given options is answer.