High School

A pilot wants to fly on a bearing of 78.9°. By flying due east, she finds that a 59.1-mph wind, blowing from the south, puts her on course.

Find the airspeed and the groundspeed of the plane.

The airspeed is ___ mph. (Round to the nearest integer as needed.)

Answer :

By using the Pythagorean theorem, the airspeed is approximately 312 mph, and the groundspeed is approximately 306 mph.

Given:

Desired bearing = 78.9°

Wind speed = 59.1 mph

We want to find the airspeed (A) and groundspeed (G) of the plane.

Calculate the Groundspeed (G):

The angle between the plane's heading and the wind direction is the difference between the desired bearing (78.9°) and 90° (since east is 90°):

Angle = 78.9° - 90° = -11.1°

Convert the angle to radians:

-11.1° = -11.1 x (π / 180)

Calculate the sine of the angle:

sin(-11.1°) ≈ -0.193

Calculate the absolute value of the groundspeed (since speed cannot be negative):

G = Wind speed / |sin(-11.1°)| ≈ 59.1 / 0.193 ≈ 306.19 mph

Calculate the Airspeed (A):

Using the Pythagorean theorem:

A² = G² + Wind speed²

A² = (306.19)² + (59.1)²

A² ≈ 93837.29 + 3499.81

A² ≈ 97337.10

A ≈ √97337.10 ≈ 311.96 mph

Rounding to the nearest integer, the airspeed is approximately 312 mph.

So, after calculating, the airspeed is approximately 312 mph, and the groundspeed is approximately 306 mph.

To know more about Pythagorean theorem, follow the link:

https://brainly.com/question/28361847

#SPJ4

Other Questions