You have the following data: A plane flying at its maximum speed can go 190 miles per hour with a tailwind or 150 miles per hour into a headwind.
(a) What is the wind speed?
Vp + Vw = 190
Vp - Vw = 150
Subtract the Eqs:
0 + 2Vw = 40
Vw = 20 mi/h.
Alternate Method:
Vw = (Vmax-Vmin)/2=(190-150) / 2=20 mi/h
To find the wind speed, we need to use the concept of relative velocity. The relative velocity is the difference between the actual speed of the plane and its speed with either a headwind or a tailwind.
Let's assume the actual speed of the plane is x miles per hour (mph), and the wind speed is y mph. With a tailwind, the plane's speed becomes x + y mph, and with a headwind, the speed becomes x - y mph.
We are given that the plane's speed with a tailwind is 190 mph, so we can set up the equation:
x + y = 190
Similarly, the speed of the plane with a headwind is given as 150 mph, so we can set up a second equation:
x - y = 150
To find the wind speed, we can solve these two equations simultaneously. There are several methods to do this, such as substitution or elimination. Here, we will use the elimination method.
By adding the two equations together, we can eliminate the variable y:
(x + y) + (x - y) = 190 + 150
2x = 340
x = 340/2
x = 170
Now, substitute the value of x back into one of the original equations to find the value of y:
170 + y = 190
y = 190 - 170
y = 20
Therefore, the wind speed is 20 mph.