Questions: A pedestrian walks 7.4 kilometers west and then 9.2 kilometers south. What is the magnitude of the pedestrian's resultant vector? Hint: Draw a vector diagram. vecR=[?] kilometers Round your answer to the nearest hundredth.

A pedestrian walks 7.4 kilometers west and then 9.2 kilometers south. What is the magnitude of the pedestrian's resultant vector?
Hint: Draw a vector diagram.
vecR=[?] kilometers

Round your answer to the nearest hundredth.

Transcript text: A pedestrian walks 7.4 kilometers west and then 9.2 kilometers south. What is the magnitude of the pedestrian's resultant vector? Hint: Draw a vector diagram. \[ |\vec{R}|=[?] \text { kilometers } \] Round your answer to the nearest hundredth.

Solution

Solution Steps

Step 1: Understand the Problem

The problem involves finding the magnitude of the resultant vector when a pedestrian walks 7.4 kilometers west and then 9.2 kilometers south. This can be visualized as a right triangle where the legs are the distances walked west and south.

Step 2: Apply the Pythagorean Theorem

To find the magnitude of the resultant vector, we use the Pythagorean theorem. The legs of the right triangle are 7.4 km (west) and 9.2 km (south). The magnitude of the resultant vector, \( |\vec{R}| \), is the hypotenuse of this triangle.

\[ |\vec{R}| = \sqrt{(7.4)^2 + (9.2)^2} \]

Step 3: Calculate the Magnitude

Calculate the squares of the distances:

\[ 7.4^2 = 54.76 \] \[ 9.2^2 = 84.64 \]

Add these values:

\[ 54.76 + 84.64 = 139.4 \]

Take the square root to find the magnitude:

\[ |\vec{R}| = \sqrt{139.4} \approx 11.8034 \]

Step 4: Round the Result

Round the magnitude to the nearest hundredth:

\[ |\vec{R}| \approx 11.80 \]