A plane flies at 220 km/h toward the south as observed by a person on the ground. The airplane pilot measures an air velocity of 2.8 x 105 m/h south. What is the velocity of the wind that affects the plane?
220 km/hr = 2.20 * 10^5 m/hr
So, there must be a headwind of 2.8-2.2 = 0.6 * 10^5 m/hr.
That is, a wind blowing north at 60 km/hr
To find the velocity of the wind that affects the plane, we can use the concept of relative velocity.
1. First, convert the airplane's air velocity from meters per hour to kilometers per hour. Since 1 kilometer is equal to 1000 meters and 1 hour is equal to 3600 seconds, we can use the following calculation:
Air Velocity (km/h) = (2.8 x 10^5 m/h) * (1 km / 1000 m) * (1 h / 3600 s)
Plugging in the given value, we have:
Air Velocity (km/h) ≈ 77.8 km/h (rounded to one decimal place)
2. Now, consider the components of the plane's velocity. The observed velocity of the plane relative to the observer on the ground is 220 km/h south, and the air velocity measured by the pilot is 77.8 km/h south.
3. The difference between the observed velocity and the air velocity gives us the velocity of the wind:
Velocity of the Wind = Observed Velocity - Air Velocity
Plugging in the given values:
Velocity of the Wind = 220 km/h south - 77.8 km/h south
Velocity of the Wind ≈ 142.2 km/h south (rounded to one decimal place)
Therefore, the velocity of the wind that affects the plane is approximately 142.2 km/h south.