An airplane has a velocity relative to the ground of 214 m/s toward the east. The pilot measures his airspeed (the speed of the plane relative to the air) to be 162 m/s. What is the minimum wind velocity possible?
The minimum wind velocity that can increase the ground speed that much is a 214-162 = 52 m/s tail wind.
To determine the minimum wind velocity possible, we need to understand the relationship between the airplane's velocity relative to the ground, its airspeed, and the wind velocity.
Let's assume the wind velocity is represented by "w" (toward the west). Therefore, the airplane's velocity relative to the ground is equal to the sum of its airspeed and the wind velocity.
Given:
Airplane's velocity relative to the ground (v) = 214 m/s (toward the east)
Airplane's airspeed (a) = 162 m/s
We can write the equation for the airplane's velocity relative to the ground as:
v = a + w
Now, let's rearrange this equation to solve for the wind velocity (w):
w = v - a
Substituting the given values into the equation:
w = 214 m/s - 162 m/s
Calculating this:
w = 52 m/s
Therefore, the minimum wind velocity possible is 52 m/s toward the west.