An airplane, after 1 hour in the air, arrives at a point 350 miles south of its departure point. There was a steady wind of exactly 25 mph from the northwest during the entire flight. Which represents the airplane's average air speed?
Please can someone help?
To find the airplane's average airspeed, we need to consider the effect of the wind on its actual ground speed.
Let's assume the airplane's airspeed is represented by "x" mph. We know that the wind blows steadily at 25 mph from the northwest.
Now, if we imagine the airplane's velocity relative to the air, it will be x mph in a direction due south (since the wind does not affect this component).
However, when we consider the airplane's velocity relative to the ground (ground speed), we need to account for the wind's effect. Since the wind blows from the northwest, it will push the airplane towards the southeast.
To calculate the ground speed, we can use vector addition. We can break down the airplane's airspeed into two components: one due south and the other due east (opposite to the wind).
The south component of the airplane's airspeed (relative to the ground) remains constant at x mph. The east component of the airplane's airspeed (relative to the ground) is the speed of the wind, which is 25 mph.
Now, since the airplane lands 350 miles south of its departure point after 1 hour, we can set up the following equation:
Ground speed = (south component of airspeed) + (east component of airspeed)
Ground speed = x mph + 25 mph
From the information given, we know that the plane flies for 1 hour, so the ground speed will be equal to the distance traveled.
350 miles = (x mph + 25 mph) * 1 hour
To solve for x (airspeed), we can rearrange the equation:
(x mph + 25 mph) * 1 hour = 350 miles
x mph + 25 mph = 350 miles/hour
x mph = 350 mph - 25 mph
x mph = 325 mph
Therefore, the airplane's average airspeed is 325 mph.