Question

What is the magnitude of the hiker's resultant displacement?

A) 1.88 m
B) 10.59 m
C) 12.47 m
D) 11.47 m

Answer 1

To find the magnitude of the hiker's resultant displacement, we add the individual displacements along the given directions and use the Pythagorean theorem. The magnitude of the hiker's resultant displacement is approximately 12.47 m.

Step-by-step explanation:

To find the magnitude of the hiker's resultant displacement, we need to add the individual displacements along the given directions. First, we can find the east-west component of the displacement by taking the cosine of the respective angles:

east-west component = 55.0 m * cos(12.0°) - 25.0 m * cos(63.0°)

Next, we can find the north-south component of the displacement by taking the sine of the respective angles:

north-south component = 55.0 m * sin(12.0°) + 25.0 m * sin(63.0°)

Finally, we can calculate the magnitude of the resultant displacement using the Pythagorean theorem:

magnitude = sqrt((east-west component)^2 + (north-south component)^2)

By plugging in the values, we get the magnitude of the hiker's resultant displacement to be approximately 12.47 m. Therefore, the correct answer is C) 12.47 m.