Question

A plane is flying due west at 34 m/s. It encounters a wind blowing at 19 m/s south. Find the resultant veloci

Answer 1

Answer:

The resultant velocity has a magnitude of 38.95 m/s

Explanation:

Vector Addition

Given two vectors defined as:

$\vec v_1=(x_1,y_1)$

$\vec v_2=(x_2,y_2)$

The sum of the vectors is:

$\vec v=(x_1+x_2,y_1+y_2)$

The magnitude of a vector can be calculated by

$d=\sqrt{x^2+y^2}$

Where x and y are the rectangular components of the vector.

We have a plane flying due west at 34 m/s. Its velocity vector is:

$\vec v_1=(-34,0)$

The wind blows at 19 m/s south, thus:

$\vec v_2=(0,-19)$

The sum of both velocities gives the resultant velocity:

$\vec v =(-34,-19)$

The magnitude of this velocity is:

$d=\sqrt{(-34)^2+(-19)^2}$

$d=\sqrt{1156+361}=\sqrt{1517}$

d = 38.95 m/s

The resultant velocity has a magnitude of 38.95 m/s