Chapter 2.4, Problem 34PP

To determine

To Find: The new ship’s position after 1.5h, relative to the starting point A.

Answer to Problem 34PP

  $112\mathrm{km}$

Explanation of Solution

Given:

The average velocity of new ship is $58\text{km/h}$ .

The distance between points A and Bis 25 km.

Formula used:

The average velocity of a particle is given by

  $\overline{v}=\frac{\Delta d}{\Delta t}=\frac{d_{final}-d_{initial}}{t_{final}-t_{initial}}$

Calculation:

Using the above formula of average velocity distance travelled by new ship in $1.5\text{h}$ is

  $\overline{v}{\text{'}}_{\text{constant}}=\frac{x\text{'}-x_B}{t\text{'}-t_B}$

Using,

  ${\overline{v}}_{\text{constant}}=58\text{km/h}$

  $t\text{'}-t_B=1.5\text{h}$

  $\begin{array}{c}x\text{'}-x_B=58\times 1.5\\ =87\mathrm{km}\end{array}$

Hence, the distance travelled by new ship with respect to the initial position A is

  $\begin{array}{c}x{\text{'}}_A=25+\left(x\text{'}-x_B\right)\\ =\left(25+87\right)\mathrm{km}\\ =112\mathrm{km}\end{array}$

Conclusion:

Thus, the new ship’s position after 1.5h, relative to the starting point A is $112\mathrm{km}.$