Question

A plane is flying with an airspeed of 190 miles per hour and heading 155°. The wind currents are running at 40 miles per hour at 160° clockwise from due north. Use vectors to find the true course and ground speed of the plane. (Round your answers to the nearest ten for the speed and to the nearest whole number for the angle.)

Answer 1

To find the true course and ground speed of the plane, we can use vector addition by considering the plane's airspeed and the wind currents as separate vectors. The true course of the plane is the direction in which it is actually moving relative to the ground. The ground speed is the magnitude of the resultant vector of the plane's airspeed and the wind speed.

Step-by-step explanation:

To find the true course and ground speed of the plane, we can use vector addition by considering the plane's airspeed and the wind currents as separate vectors. The true course of the plane is the direction in which it is actually moving relative to the ground. The ground speed is the magnitude of the resultant vector of the plane's airspeed and the wind speed.

First, we need to find the x and y components of the plane's airspeed and the wind speed. Using the given information, we can calculate:

Airspeed x-component = 190 mph * cos(155°)

Airspeed y-component = 190 mph * sin(155°)

Wind speed x-component = 40 mph * cos(160°)

Wind speed y-component = 40 mph * sin(160°)

Next, we add the corresponding components to find the resultant vector:

Resultant x-component = Airspeed x-component + Wind speed x-component

Resultant y-component = Airspeed y-component + Wind speed y-component

Finally, we can find the true course by taking the arctangent of the y-component divided by the x-component:

True course = arctan(Resultant y-component / Resultant x-component)

And the ground speed is the magnitude of the resultant vector:

Ground speed = sqrt((Resultant x-component)^2 + (Resultant y-component)^2)