Chapter 6.3, Problem 38SSC

To determine

The speed of the plane along with the direction relative to the ground.

Answer to Problem 38SSC

The relative velocity of the plane with respect to ground $v_{\text{p/g}}$ is equal to $300\text{km/h}$ and its direction is North East.

Explanation of Solution

Given:

The velocity of the airplane due north relative to the air is $235\text{km /h}$ .

The velocity of the wind due northeast relative to the ground is $65\text{km /h}$ .

Formula used:

Vector addition ,

$v_{\text{a/b}}+v_{\text{b/c}}=v_{\text{a/c}}$

Calculation:

The free body diagram of the motion of airplane and the wind is shown below.

Relative velocity of air plane with respect to air $v_{\text{p/a}}=235\text{km/h}$ .

Relative velocity of the wind with respect to ground $v_{\text{w/g}}=65\text{km/h}$ .

The relative velocity of the plane with respect to ground $v_{\text{p/g}}$ is,

  $v_{\text{p/g}}=v_{\text{p/a}}+v_{\text{w/g}}$

  $\begin{array}{c}{v}_{\text{p/g}}=235\text{km/h}+65\text{km/h}\\ v_{\text{p/g}}\text{= 300km/h}\end{array}$

The direction of relative velocity is North East.

Conclusion:

Thus, the relative velocity of the plane with respect to ground $v_{\text{p/g}}$ is equal to $300\text{km/h}$ and its direction is North East.