An airplane that can fly at 300 km/hr is flying at 210 when it is hit by a wind of 125 km/hr at 110. What is the new velocity of the plan?

To find the new velocity of the plane, we need to consider the combined effect of the airplane's original velocity and the wind speed.

First, let's break down the given information:

- The airplane can fly at a speed of 300 km/hr.
- The airplane's original velocity is 210 km/hr.
- The wind is blowing at a speed of 125 km/hr.
- The direction of the wind is given as 110, which indicates the angle relative to the airplane's original direction.

To find the new velocity, we can use vector addition, which involves adding the components of velocity in each direction.

1. Break the original velocity and the wind speed into horizontal and vertical components:
- Original velocity components:
- Horizontal component = original velocity * cos(theta), where theta is the angle between the original velocity vector and the x-axis.
- Vertical component = original velocity * sin(theta), where theta is the angle between the original velocity vector and the x-axis.
- Wind speed components:
- Horizontal component = wind speed * cos(phi), where phi is the angle between the wind speed vector and the x-axis.
- Vertical component = wind speed * sin(phi), where phi is the angle between the wind speed vector and the x-axis.

2. Add the horizontal components of the velocities:
- New horizontal velocity = original velocity's horizontal component + wind speed's horizontal component.

3. Add the vertical components of the velocities:
- New vertical velocity = original velocity's vertical component + wind speed's vertical component.

4. Calculate the magnitude and direction of the new velocity:
- The magnitude of the new velocity is given by the Pythagorean theorem:
- New speed = sqrt((New horizontal velocity)^2 + (New vertical velocity)^2).
- The direction of the new velocity can be found using inverse tangent:
- New angle = atan2((New vertical velocity), (New horizontal velocity)).

5. Round the magnitude and direction of the new velocity to the desired level of precision.

By following these steps, you can determine the new velocity of the plane after being hit by the wind.