A pilot is flying at a speed of 300 miles per hour and the wind is blowing due north at 50 miles per hour.What is the magnitude of the resultant velocity of the plane?
depends on which direction the plane is heading. The speed could be anywhere between 250 and 350 mph.
300 mph on what heading?
Usually you give the direction a wind is coming from, like a North wind caries you south.
Here do you mean it blows you North?
In any case use vector components
North component = 50 + 300 cos A
East component = 300 sin A
where A is the heading angle clockwise from north
magnitude = sqrt(north comp^2+east comp^2)
To find the magnitude of the resultant velocity of the plane, we can use vector addition. We need to consider the velocity of the plane and the velocity due to the wind.
The velocity of the plane can be represented as a vector with a magnitude of 300 miles per hour, pointing in the direction of the plane's motion.
The velocity due to the wind can be represented as a vector with a magnitude of 50 miles per hour, pointing due north.
To find the resultant velocity, we can add these two vectors using vector addition. Since the wind is blowing due north, the two vectors are perpendicular to each other, and we can use the Pythagorean theorem to calculate the magnitude of the resultant velocity.
Let's label the velocity of the plane as vector A and the velocity due to the wind as vector B.
Magnitude of vector A (velocity of the plane) = 300 miles per hour
Magnitude of vector B (velocity due to the wind) = 50 miles per hour
Using the Pythagorean theorem, we can calculate the magnitude of the resultant velocity (vector C):
C^2 = A^2 + B^2
C^2 = 300^2 + 50^2
C^2 = 90000 + 2500
C^2 = 92500
Taking the square root of both sides, we find:
C = √92500
C ≈ 304.1
Therefore, the magnitude of the resultant velocity of the plane is approximately 304.1 miles per hour.
To find the magnitude of the resultant velocity of the plane, we can use vector addition. The velocity of the plane is a vector in the southward direction (opposite to the northward wind), and the magnitude of this velocity is 300 miles per hour. The wind velocity is a vector in the northward direction, and its magnitude is 50 miles per hour.
To add these two vectors, we can use the Pythagorean theorem. The magnitude of the resultant velocity (V) can be found using the equation:
V^2 = (velocity of plane)^2 + (velocity of wind)^2
Plugging in the given values, we have:
V^2 = (300 miles/hour)^2 + (50 miles/hour)^2
V^2 = 90000 + 2500
V^2 = 92500
Taking the square root of both sides, we find:
V ≈ 304.14 miles/hour
Therefore, the magnitude of the resultant velocity of the plane is approximately 304.14 miles per hour.