Chapter 6.3, Problem 26PP

To determine

The speed of the person relative to the street.

Answer to Problem 26PP

  $6.0\text{ m/s}$

Explanation of Solution

Given:

A bus is moving at a speed of 2.0m/s with respect to the street and a person is moving to the front of the bus at 4.0m/s relative to the bus.

Formula used:

Relative velocity of an object a to object c is given by

  $v_{a/c}=v_{a/b}+v_{b/c}$

Calculation:

The speed of the person relative to the street can be written as:

  $v{\text{person/street}}_{}=v_{\text{person/bus}}+v_{\text{bus/street}}$

Using given values in above,

  $\begin{array}{c}v{\text{person/street}}_{}=\left(4.0+2.0\right)\text{m/s}\\ v{\text{person/street}}_{}=6.0\text{ m/s}\end{array}$

Conclusion:

Thus, the speed of the person with respect to the street is $6.0\text{ m/s}$ .