Chapter 6.3, Problem 32SSC

To determine

Speed and direction of airplane relative to ground.

Answer to Problem 32SSC

  $260\text{km/h}$ westwards

Explanation of Solution

Given:

Speed of plane relative to air is $v_{pa}=285\text{km/h}$ towards west

Speed of wind relative to ground is $v_{ag}=25\text{km/h}$ towards east

Formula Used:

Relative velocity of airplane with respect to ground can be obtained by:

  $v_{pg}=v_{pa}+v_{ag}$

Where, $v_{pa}$ is velocity of plane relative to air and $v_{ag}$ is velocity of air with respect to ground.

Calculations:

Speed of plane relative to ground is

  $\begin{array}{l}{v}_{pg}=v_{pa}+v_{ag}\\ =285\text{km/h}-25\text{km/h}\\ =260\text{km/h}\left(\text{westwards}\right)\end{array}$

Conclusion:

Speed and direction of airplane relative to ground is $260\text{km/h}$ westwards.