Answer to Question #230989 in Physics for Sweet Pea

Question

 A plane flying due north at 2.00 x 10^2 mph encounters winds which blow the plane due south at 45 mph. Determine the plane's resultant velocity (magnitude and direction).

Answer 1

Let's take north as a positive direction. Then, plane's resultant velocity is the vector sum of two velocities: the velocity of the plane and the velocity of the wind:

$$\vec{v}_{res}=\vec{v}_{plane}+\vec{v}_{wind},$$ $$v_{res}=v_{plane}-v_{wind}=200\ mph-45\ mph=155\ mph.$$

The sign plus means that the plane's resultant velocity directed to the north.

Answer:

$v_{res}=155\ mph,$ to the north.