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

V = 308.06 miles/hour

θ = 13.13° west of north.

Step-by-step 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.