Question

A disoriented physics professor drives 3.27km north, then 4.69km west, and then 1.59km south.

Use components to find the magnitude of the resultant displacement of this professor.

Answer 1

To find the magnitude of the resultant displacement, we can break down each individual displacement into their north and west components. By calculating the magnitude of the resultant displacement using the Pythagorean theorem, we find that it is approximately 5.72 km.

Step-by-step explanation:

To find the magnitude of the resultant displacement, we need to break down each individual displacement into its north and west components. The professor drove 3.27 km north, which gives us a north component of 3.27 km. The professor then drove 4.69 km west, which gives us a west component of -4.69 km (negative because it's in the opposite direction of east). Finally, the professor drove 1.59 km south, which gives us a south component of -1.59 km.

Now we can find the resultant displacement by adding the north and west components:

North Component: 3.27 km

West Component: -4.69 km

Resultant Displacement = √((3.27 km)^2 + (-4.69 km)^2)

Resultant Displacement = √(10.6929 km^2 + 21.9961 km^2)

Resultant Displacement = √(32.6890 km^2)

Resultant Displacement = 5.7177 km

Therefore, the magnitude of the resultant displacement is approximately 5.72 km.