Chapter 5, Problem 91A

To determine

The largest and smallest possible net displacement and its sketches.

Answer to Problem 91A

Largest possible displacement is 7 and smallest possible displacement is 1.

Explanation of Solution

Given info:

$\begin{array}{l}{v}_1=4\\ v_2=3\end{array}$

Calculation:

Largest possible net displacement will be obtained when both component vectors lie in the same direction as shown in figure

Then net vector can be determined as

$\begin{array}{c}\text{net displacement}={\text{ v}}_{\text{1}}+{\text{v}}_2\\ =\text{3}+\text{4}\\ =\text{7}\end{array}$

Smallest possible net displacement will be obtained when component vectors lie in opposite direction as shown in figure, so that time net vector can be determined as

$\begin{array}{c}\text{net displacement}={\text{ v}}_{\text{2}}{\text{-v}}_1\\ =\text{4-3}\\ =\text{1}\end{array}$

Conclusion:Largest possible displacement is 7 and smallest possible displacement is 1.