Chapter 5, Problem 18A

For Questions 18—19, recall that when two vectors in the same or exactly opposite directions are added, the magnitude of their resultant is the sum or difference of their original magnitudes.

Calculate the resultant velocity of an air-plane that normally flies at 200 km/h if it encounters a 50-km/h tailwind. If it encounters a 50-km/h headwind.

To determine

Resultant velocity of airplane.

Answer to Problem 18A

Resultant velocity is 250 km/h when encounters tailwind and 150 km/h when encounters headwind.

Explanation of Solution

Given :

Velocity of airplane, $v_a=200\text{ km/h}$ ,velocity of wind which encounters tail of airplane is $v_{w1}=50\text{ km/h}$ and velocity of wind which encounters head of airplane is, $v_{w2}=50\text{ km/h}$

Formula used :

According to concept of relative velocity.

  $v=v_a+v_w$ …..(1)

Where, $v_a\text{ and }{v}_w$ are velocity of airplane and velocity of wind in same direction.

  $v=v_a-v_w$ ……(2)

Where, $v_a\text{ and }{v}_w$ are velocity of airplane and velocity of wind in opposite direction .

Calculation :

Substituting the value of $v_a$ and $v_w=v_{w1}$ in equation (1).

  $\begin{array}{l}v=200+50\\ =250\text{ km/h}\end{array}$

Now, substituting the value of $v_a$ and $v_w=v_{w2}$ in equation (2).

  $\begin{array}{l}v=200-50\\ =150\text{ km/h}\end{array}$

Conclusion :

Therefore, resultant velocity of airplane when it encounters tailwind is 250 km/h and 150 km/h when it counters headwind