Chapter 6.3, Problem 31PP

a.

To determine

Velocity of airplane relative to ground.

Answer to Problem 31PP

  $v_{pg}=250\text{km/h}$

Explanation of Solution

Given:

Speed of plane relative to air is $v_{pa}=200\text{km/h}$

Tailwind is $v_{ag}=50\text{km/h}$

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:

Since tailwind is in plane’s direction. So, velocity of plane relative to ground is given as

  $\begin{array}{c}{v}_{pg}=v_{pa}+v_{ag}\\ =200+50\\ =250\text{km/h}\end{array}$

Conclusion:Velocity of airplane relative to ground is $v_{pg}=250\text{km/h}$ .

b.

To determine

Velocity of plane relative to ground.

Answer to Problem 31PP

  $v_{pg}=150\text{km/h}$

Explanation of Solution

Given:

Velocity of plane relative to air is $v_{pa}=200\text{km/h}$

Headwind is $v_{ag}=50\text{km/h}$

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:

Since headwind is opposite to plane’s direction. So, velocity of plane relative to ground is given as,

  $\begin{array}{c}{v}_{pg}=v_{pa}+v_{ag}\\ =200+\left(-50\right)\\ =150\text{km/h}\end{array}$

Conclusion:Velocity of plane relative to ground $v_{pg}=150\text{km/h}$ .