1. a plane has heading of 54 degrees & airspeed of 225mph. The wind is blowing at 33mph from 144 degrees. what are its actua heading & airspeed? Round to one decimal place.
A) 61.4deg, 257.1mph B) 7.4deg, 66114.0mph C) 136.6deg, 288mph D) no solution
Vp = 225 mph @ 54 Deg.
Vw = 33mph @ 144 Deg.
X = hor. = 225cos54 + 33cos144,
X = 132.25 -26.7 = 105.6mph.
Y = ver. = 225sin54 + 33sin144,
Y = 182 + 19.4 = 201.4mph.
tanA = Y/X = 201.4 / 105.6 = 1.9074.
A = 62.3 Deg.
V = X/cosA = 105.6 / cos62.3 = 227.2mph
Heading: 62.3 Deg. @ 227.2mph.
Your book answer is 257mph. Check for
typos.
To find the actual heading and airspeed of the plane, we need to consider the effect of the wind on the plane's motion.
Step 1: Decompose the wind vector
First, we need to break down the wind vector into its east-west (crosswind) and north-south (headwind or tailwind) components.
Given:
- Wind speed = 33 mph
- Wind direction = 144 degrees (measured clockwise from north)
To find the east-west component, we multiply the wind speed by the sin of the wind direction:
East-West Component = 33 mph * sin(144 degrees)
To find the north-south component, we multiply the wind speed by the cosine of the wind direction:
North-South Component = 33 mph * cos(144 degrees)
Step 2: Add wind components to the plane's direction and speed
To find the actual heading, we add the wind's east-west component to the plane's heading:
Actual Heading = Plane Heading + East-West Component
To find the actual airspeed, we add the wind's north-south component to the plane's airspeed:
Actual Airspeed = Plane Airspeed + North-South Component
Given:
- Plane Heading = 54 degrees
- Plane Airspeed = 225 mph
Calculations:
East-West Component = 33 mph * sin(144 degrees)
North-South Component = 33 mph * cos(144 degrees)
Actual Heading = 54 degrees + East-West Component
Actual Airspeed = 225 mph + North-South Component
Perform the calculations to find the actual heading and airspeed.
The correct choice is A) 61.4 degrees, 257.1 mph