Chapter 6, Problem 5STP

To determine

The velocity of jogger relative to the boat.

Answer to Problem 5STP

B. $30\text{km/h}$

Explanation of Solution

Given:

The boat is traveling east at $20\text{km/h}$ towards the jogger, thus $v_{\text{boat/ground}}=20\text{}\text{km/h}$

While jogger is running west at $10\text{km/h}$ , thus $v_{\text{jogger/ground}}=10\text{km/h}$

Formula used:

The relative velocity of an object a to object c is given by

  $v_{a/c}=v_{a/b}+v_{b/c}$

Calculation:

Assume the west direction to be positive then the east direction will be negative. Then, the given velocities can be written as,

  $v_{\text{jogger/ground}}=10\text{km/h}$

  $v_{\text{boat/ground}}=-20\text{}\text{km/h}$

Now, the velocity of jogger relative to the boat can be written as,

  $\begin{array}{c}v{\text{jogger/boat}}_{}=v_{\text{jogger/ground}}+v_{\text{ground/boat}}\\ v{\text{jogger/boat}}_{}=v_{\text{jogger/ground}}-v_{\text{boat/ground}}\end{array}$

Using given values in above,

  $\begin{array}{c}v{\text{jogger/boat}}_{}=v_{\text{jogger/ground}}-v_{\text{boat/ground}}\\ v{\text{jogger/boat}}_{}=10-\left(-20\right)\\ v{\text{jogger/boat}}_{}=30\text{km/h}\end{array}$

Conclusion:

Thus, the velocity of jogger relative to the boat is $30\text{km/h}$ .