Chapter 4, Problem 20A

Jogging Jake runs along a train flatcar that moves at the velocities shown. From greatest to least, rank the relative velocities of Jake as seen by an observer on the ground. (Call the direction to the right positive.)

To determine

To rank: The relative velocities of person J , from greatest to least, as seen by an observer on the ground.

Answer to Problem 20A

D> C > A > B

Explanation of Solution

Given:

The given figure representing the velocity of person J at different locations is shown below.

Right direction is considered positive.

Formula used:

Relative velocity with respect to the observer on the ground is the vector sum of person J speed and the train flatcar.

$\stackrel{\rightharpoonup }{v_o}=\overrightarrow{v_t}+\overrightarrow{v_J}$

Calculation:

Calculate the relative velocity at each position if right direction is considered positive.

For case A,

  $\begin{array}{c}\overrightarrow{v_o}=8-4\\ =4\text{m/s}\end{array}$

For case B,

  $\begin{array}{c}\overrightarrow{v_o}=-10+6\\ =-4\text{m/s}\end{array}$

For case C,

  $\begin{array}{c}\overrightarrow{v_o}=6+4\\ =10\text{m/s}\end{array}$

For case D,

  $\begin{array}{c}\overrightarrow{v_o}=18-6\\ =12\text{m/s}\end{array}$

At D, relative velocity is maximum and at B, relative velocity is minimum.

Conclusion:

Therefore, the ranking of relative velocities is D> C > A > B.