Chapter 5, Problem 20A

For Questions 20—21, recall that the resultant V of two vectors A and B at right angles to each other is found using the Pythagorean theorem: $V=\sqrt{A^2+B^2}$

Calculate the resulting speed of an airplane with an airspeed of 120 km/h pointing due north when it encounters a wind of 90 km/h directed from the west. (Recall, speed is the magnitude of velocity.)

To determine

Magnitude of resultant speed of airplane.

Answer to Problem 20A

Resultant velocity is, $v=150\text{ km/h}$

Explanation of Solution

Given :

Velocity of airplane in north direction is, $v_a=120\text{ km/h}$

Formula used :

  $R=\sqrt{A^2+B^2}$

Where, R is resultant vector, A and B are two vectors which are perpendicular to each other.

Calculation :

Velocity of airplane and velocity of wind is represented by below figure.

  

Here, both velocity are perpendicular to each other.

Therefore, magnitude of their resultant velocity will be,

  $v=\sqrt{v_a^2+v_w^2}$

Now, substituting the value of $v_a$ and $v_w$ solve.

  $\begin{array}{l}v=\sqrt{{120}^2+{90}^2}\\ =\sqrt{14400+8100}\\ =150\text{ km/h}\end{array}$

Conclusion :

Therefore, magnitude of resultant velocity airplane is 150 km/h.