An airplane flies due north at 160 km/h with respect to the air. There is a wind blowing at 80 km/h to the east relative to the ground. What is the plane's speed relative to the ground?
X=160sin0+80sin45=56.57km/h
Y=160cos0+80cos45=216.57km/h
Vr=sqrt(X^2+Y^2)=223.84km/hr
Tan A = X/Y, A = Degrees CW = Direction
To find the plane's speed relative to the ground, we need to use vector addition.
First, let's break down the airplane's velocity into its north and east components relative to the ground.
The airplane's velocity relative to the ground in the north direction would be 160 km/h. Since there is no wind blowing in the north direction, this component remains the same.
The airplane's velocity relative to the ground in the east direction would be the sum of its velocity due to the wind and its own velocity in the east direction. The wind is blowing at 80 km/h to the east, and since it affects the airplane's movement in the east direction, the airplane's velocity relative to the ground in the east direction would be 80 km/h.
Now, we can use the Pythagorean theorem to find the magnitude of the airplane's velocity relative to the ground:
Magnitude = √(North component^2 + East component^2)
= √(160 km/h^2 + 80 km/h^2)
= √(25600 km^2/h^2 + 6400 km^2/h^2)
= √(32000 km^2/h^2)
= 178.89 km/h (rounded to 2 decimal places)
Therefore, the plane's speed relative to the ground is approximately 178.89 km/h.
To find the plane's speed relative to the ground, we can use the concept of vector addition.
First, imagine the airplane's velocity as a vector pointing due north with a magnitude of 160 km/h. Let's call this vector "V_airplane".
Next, consider the wind blowing to the east relative to the ground. We can represent the wind's velocity as a vector pointing due east with a magnitude of 80 km/h. Let's call this vector "V_wind".
To find the plane's speed relative to the ground, we need to find the resultant vector of the airplane's velocity and the wind's velocity. This can be done by adding the vectors V_airplane and V_wind.
Since the wind is blowing to the east, which is perpendicular to the north direction in which the airplane is flying, we can treat the vectors as a right-angled triangle. The magnitude of the resultant vector can be found using the Pythagorean theorem.
Let's denote the magnitude of the resultant vector as "V_resultant".
Using the Pythagorean theorem, we can calculate V_resultant as follows:
V_resultant^2 = V_airplane^2 + V_wind^2
Plugging in the given values:
V_resultant^2 = (160 km/h)^2 + (80 km/h)^2
V_resultant^2 = 25600 km^2/h^2 + 6400 km^2/h^2
V_resultant^2 = 32000 km^2/h^2
Taking the square root of both sides:
V_resultant = √32000 km/h
V_resultant ≈ 178.89 km/h
Therefore, the airplane's speed relative to the ground is approximately 178.89 km/h.