Question

An airplane has a maximum airspeed velocity of 140 mph South. If the wind is 60 mph West, what is the resultant velocity (groundspeed) and direction of the airplane?

Answer 1

R∠ is 152,3 ∠ 246,8

Answer 2

R∠ is 152,3 ∠ 246,8

Step-by-step explanation:

We need to add (vectorially) these two velocities. We can choose the coordinates system just that speed of the airplane is the negative part of the y-axis, and negative region of the x-axis, for wind speed, according to

this, the module of the resultant velocity R is:

R =√ (60)² + (140)²

R = √( 3600) + ( 19600)

R =√ 23200

R = 152,315 mph

The tangent of the angle (α ) between R and the y-axis is:

tan α = 60/140

tan α = 0,4286

From tangent tables, we get arctan 0.4286

α = 23,2⁰

Then R∠ is 152,3 ∠ 246,8