Question

An airplane is trying to fly at a speed of 300 miles per hour straight North, but a 70 miles per hour wind is blowing toward the west. What is the speed of the plane when these two velocity vectors are added together?

Answer 1

Answer:

                          V = 308.06 miles/hour

                          θ = 13.13°  west of north.

Explanation:

Airplane speed = V₁ = 300 miles/hour    

Wind speed = V₂ = 70 miles/hour

Resultant speed of the plane = V = ?

As airplane is trying to fly straight North and wind is blowing toward the west. So the angle between airplane velocity and wind velocity is 90°.

By Pythagoras Theorem

                            V =$\sqrt{V_{1}^{2}+V_{2}^{2} }$

                            V = $\sqrt{300^{2}+70^{2} }$

                            V = 308.06 miles/hour

                            θ = tan⁻¹(70/300)

                            θ = 13.13°  west of north.