The pilot of a plane measures an air velocity of 186 km/h south. An observer on the ground sees the plane pass overhead at a velocity of 102 km/h toward the north.
A.) What is the velocity of the wind that is affecting the plane? Let north be positive. Answer in units of km/h
To determine the velocity of the wind, we need to find the difference between the velocity of the plane as measured by the pilot and the velocity of the plane observed by the ground observer. The wind velocity affects the plane's motion and can be calculated by taking the difference between the two velocities.
Given:
Velocity measured by the pilot, v_pilot = 186 km/h south (negative velocity as south is opposite to the chosen positive direction)
Velocity observed by the ground observer, v_observer = 102 km/h north (positive velocity as north is the chosen positive direction)
To calculate the wind velocity, we subtract the observer's velocity from the pilot's velocity, remembering to pay attention to the chosen positive direction:
Wind velocity, v_wind = v_pilot - v_observer = 186 km/h south - 102 km/h north
We need to make sure both velocities have the same direction. Since 186 km/h south is equivalent to -186 km/h north (-ve sign indicates opposite direction), we can rephrase the subtraction as:
v_wind = -186 km/h north - 102 km/h north
Now we can simplify and perform the subtraction:
v_wind = -288 km/h north
Thus, the velocity of the wind affecting the plane is 288 km/h north. Note that the negative sign indicates that the wind is blowing in the opposite direction to the plane's movement.
To find the velocity of the wind affecting the plane, we need to take the difference between the velocity measured by the pilot and the velocity observed by the observer on the ground.
Given:
Velocity measured by the pilot = 186 km/h south
Velocity observed by the observer = 102 km/h north
We can consider the direction of the wind to be opposite to the direction observed by the pilot. Therefore, the velocity of the wind can be calculated as follows:
Magnitude of the velocity of the wind = Magnitude of the velocity measured by the pilot - Magnitude of the velocity observed by the observer
= 186 km/h - 102 km/h
= 84 km/h
Since the wind is affecting the plane in the opposite direction to the observed velocity, the velocity of the wind is 84 km/h north.