What is the resulting velocity of an airplane flying east at 100 knots when there is a wind blowing from the south at 75 knots?
Velocity Calculation:
The airplane's resulting velocity is 125 knots, heading east.
The magnitude of the airplane vector is larger (100 knots > 75 knots), so we keep its direction.
The resulting velocity of the airplane can be found by considering the wind's effect on the plane's motion.
First, let's break down the given information:
- Wind speed: 75 knots from the south
- Airplane speed: 100 knots heading east
To find the resulting velocity of the airplane, we need to add the vector velocities of the wind and the airplane.
- Convert the wind speed and the airplane speed into vector form. The wind speed vector will point to the south and have a magnitude of 75 knots. The airplane speed vector will point to the east and have a magnitude of 100 knots.
- Since the wind is blowing from the south, the wind vector will be directed in the negative y-direction.
- Add the vector velocities of the wind and the airplane. Since the wind vector is directed opposite to the airplane's direction, subtract the wind vector from the airplane vector. This can be done by adding the magnitudes and keeping the direction of the larger magnitude vector. In this case, the magnitude of the airplane vector is larger (100 knots > 75 knots), so we keep its direction, which is east.
- Now, let's find the magnitude of the resulting velocity. We can use the Pythagorean theorem to find the magnitude of the resulting velocity vector.
Resulting velocity magnitude = √((magnitude of airplane vector)^2 + (magnitude of wind vector)^2)
Resulting velocity magnitude = √((100 knots)^2 + (75 knots)^2) = √(10000 + 5625) = √(15625) = 125 knots.
Therefore, the resulting velocity of the airplane is 125 knots, and its direction is east.