A physics student adds two displacement vectors with magnitudes of 8.0 km and 6.0 km. Which one of the following statements is true concerning the magnitude of the resultant displacement?
A)It must be 10.0 km.
B)It must be 14.0 km.
C)It could be equal to zero kilometers, depending on how the vectors are oriented.
D)No conclusion can be reached without knowing the directions of the vectors.
E)It could have any value between 2.0 km and 14.0 km depending on how the vectors are oriented.

Question

Quizplus · Accepted Answer

The magnitude of the resultant displacement can be found using the Pythagorean theorem:

resultant displacement = √(8.0 km)^2 + (6.0 km)^2 
resultant displacement = √(64 km^2 + 36 km^2) 
resultant displacement = √100 km^2 
resultant displacement = 10 km

Therefore, if the two displacement vectors are added head to tail, the magnitude of the resultant displacement will be 10 km. However, if the vectors are not added head to tail, but are instead added at some angle other than 180 degrees, the magnitude of the resultant displacement could be any value between 2.0 km (if the vectors are perfectly opposed) and 14.0 km (if the vectors are perfectly aligned). Thus, the answer is E.

A Physics Student Adds Two Displacement Vectors with Magnitudes of 8.0