Chapter 2, Problem 1CQ

An insect inside a bus flies from the back toward the front at 5.0 mi/h. The bus is moving in a straight line at 50.0 mi/h. What is the speed of the insect?

To determine

The speed of the insect relative to the ground.

Answer to Problem 1CQ

The speed of the insect relative to the ground is $55\text{mi/h}$.

Explanation of Solution

Write the expression for relative speed.

    $v_{\text{ig}}=v_{\text{ib}}+v_{\text{bg}}$                                                     (I)

Here, $v_{\text{ig}}$ is the speed of insect relative to the ground, $v_{\text{ib}}$ is the speed of the insect relative to the bus and $v_{\text{bg}}$ is the speed of the bus relative to the ground.

Conclusion:

Substitute $5.0\text{mi/h}$ for $v_{\text{ib}}$ and $50.0\text{mi/h}$ for $v_{\text{bg}}$ in equation (I) to find $v_{\text{ig}}$.

    $\begin{array}{c}{v}_{\text{ig}}=5.0\text{mi/h}+50.0\text{mi/h}\\ =55.0\text{mi/h}\end{array}$

Therefore, the speed of the insect relative to the ground is $55.0\text{mi/h}$.