an airplane has a velocity of 499 km/h relative to the moving air. at the same time, a wind blows northward with a speed of 87 km/h relative to the earth. the airplane is moving in an easterly direction relative to the earth. find speed of airplane to relative to earth.
To find the speed of the airplane relative to the Earth, we need to combine the velocity of the airplane relative to the moving air with the velocity of the wind relative to the Earth.
Let's break down the velocities:
Velocity of the airplane with respect to the moving air = 499 km/h
Velocity of the wind with respect to the Earth = 87 km/h (northward)
Since the airplane is moving in an easterly direction relative to the Earth, we need to combine the velocities using vector addition.
To perform vector addition, we need to define a coordinate system. Let's assume that the east direction is positive and the north direction is positive.
1. Convert the velocity of the airplane and the wind into vector form:
Velocity of the airplane with respect to the moving air = 499 km/h (eastward)
Velocity of the wind with respect to the Earth = 87 km/h (northward)
2. Apply vector addition:
To find the resultant velocity, we need to add the vectors:
Resultant velocity = Velocity of the airplane with respect to the moving air + Velocity of the wind with respect to the Earth
In vector form:
Resultant velocity = 499 km/h (eastward) + 87 km/h (northward)
3. Use the Pythagorean theorem to calculate the magnitude of the resultant velocity:
Magnitude of the resultant velocity = sqrt((499 km/h)^2 + (87 km/h)^2)
4. Calculate the final result:
Magnitude of the resultant velocity = sqrt(248001 km^2/h^2 + 7569 km^2/h^2)
Magnitude of the resultant velocity = sqrt(255570 km^2/h^2)
Magnitude of the resultant velocity ≈ 505.55 km/h
Therefore, the speed of the airplane relative to the Earth is approximately 505.55 km/h.
the speed is the vector sum of the plane and the wind
north and east are perpendicular, so it's a right triangle
s² = 499² + 87²