Question

2) An airplane flies with a velocity v1=90 m/s to the west, but there is a crosswind of v2=40 m/s to the south.

a. What is the magnitude of the plane’s resultant velocity?
b. What is the plane’s resultant direction (from west)?

Answer 1

The magnitude of the plane's resultant velocity is approximately 98.49 m/s, and the direction is approximately 24.10° South of West.

Step-by-step explanation:

To find the resultant velocity of the plane, we can use vector addition. The magnitude of the resultant velocity can be found using the Pythagorean theorem:

Magnitude of Resultant Velocity = √(v1^2 + v2^2)

Substituting the values, we get:
Magnitude of Resultant Velocity = √(90^2 + 40^2) = √(8100 + 1600) = √9700 ≈ 98.49 m/s

To find the direction of the resultant velocity, we can use trigonometry. The direction is given by the tangent of the angle:

Resultant Direction = arctan(v2/v1)

Substituting the values, we get:
Resultant Direction = arctan(40/90) ≈ 24.10° South of West

Answer 2

the magnitude will be =23.94 WS and the direction will be =98.48 m/s