Chapter 6.3, Problem 30PP

To determine

Speed of airplane relative to ground.

Answer to Problem 30PP

  $167.70\text{ km/h}$

Explanation of Solution

Given:

Speed of airplane is $150\text{ km/h}$ due north relative to air.

Speed of wine is $75\text{ km/h}$ due east relative to ground.

Formula used:

  $R=\sqrt{P^2+Q^2}$

Here, P and Q are two vectors which are perpendicular to each other.

Calculation:

Speed of airplane relative to air due north. Let $P=150\text{ km/h}$

Graphical representation will be:

  

Now, speed of wind due east relative to ground. Let $Q=75\text{ km/h}$

Graphical representation will be:

  

Now, speed of airplane with respect to ground will be:

  

From the above figure, P and Q are perpendicular to each other.

Therefore, speed of airplane relative to ground is:

  $\begin{array}{c}R=\sqrt{P^2+Q^2}\\ =\sqrt{{150}^2+{75}^2}\\ =\sqrt{28125}\\ =167.70\text{ km/h}\end{array}$

Conclusion:

Speed of airplane with respect to ground is $167.70\text{ km/h}$ .