An airplane is heading due east.The airspeed indicator shows that the plane is moving at a speed of 370 km/h relative to the air.If the wind is blowing from the south at 92.5 km/h,the velocity of the airplane relative to the ground is
A)357 km/h at 14º east of north.
B)381 km/h at 104º east of north.
C)381 km/h at 76º east of north.
D)357 km/h at 76º east of north.
E)381 km/h at 14º east of north.

Question

Quizplus · Accepted Answer

To find the velocity of the plane relative to the ground, we need to use vector addition.

Let's call the velocity of the plane relative to the ground Vg. 
We can break this vector into two components: one parallel to the wind, and one perpendicular to the wind.

The component of Vg parallel to the wind is simply the airspeed of the plane (370 km/h) because it is not affected by the wind.

The component of Vg perpendicular to the wind is equal to the wind velocity (92.5 km/h).

We can use the Pythagorean theorem to find the magnitude of Vg:

Vg^2 = (370 km/h)^2 + (92.5 km/h)^2 
Vg = 381 km/h

To find the direction of Vg, we need to use trigonometry.

The angle between the plane's velocity and the wind direction is given by:

theta = arctan(92.5 km/h / 370 km/h) 
theta = 14 degrees

Since the plane is heading due east, we need to add 90 degrees to this angle to get the direction relative to north:

theta = 14 degrees + 90 degrees 
theta = 76 degrees

Therefore, the velocity of the airplane relative to the ground is:

381 km/h at 76 degrees east of north.

So, the answer is C.

An Airplane Is Heading Due East