A pilot wishes to reach an airport 350 Km due east from his present position. The wind is blowing from N25degreesE with a speed of 80Km/h and the planes airspeed is 400 km/h. What ground speed and what heading should the pilot steer to reach the airport? How many minutes will of take the plane to reach the airport?

To determine the ground speed and heading the pilot should steer, we will use vector addition. We can break down the velocities into their components, add them up, and then calculate the magnitude and direction of the resulting vector.

1. Find the components of the wind velocity:
- The wind is blowing from N25degreesE. Splitting this into its north and east components, we get:
Wind north component = wind speed * sin(25 degrees) = 80 km/h * sin(25 degrees)
Wind east component = wind speed * cos(25 degrees) = 80 km/h * cos(25 degrees)

2. Calculate the components of the plane's velocity:
- The plane's airspeed is 400 km/h in still air, so its velocity components can be considered as:
Plane north component = plane airspeed * sin(0 degrees) = 400 km/h * sin(0 degrees)
Plane east component = plane airspeed * cos(0 degrees) = 400 km/h * cos(0 degrees)

3. Add the components of the wind and plane's velocity vectors:
- Ground north component = Plane north component + Wind north component
- Ground east component = Plane east component + Wind east component

4. Calculate the magnitude and direction of the ground velocity vector:
- Ground speed = √(Ground north component)^2 + (Ground east component)^2
- Ground heading can be found using the arctan function: Ground heading = arctan(Ground north component / Ground east component)

5. Calculate the time to reach the airport:
- Time = Distance / Ground speed

Let's plug in the values and solve the problem:

Wind north component = 80 km/h * sin(25 degrees)
Wind east component = 80 km/h * cos(25 degrees)

Plane north component = 400 km/h * sin(0 degrees)
Plane east component = 400 km/h * cos(0 degrees)

Ground north component = Plane north component + Wind north component
Ground east component = Plane east component + Wind east component

Ground speed = √(Ground north component)^2 + (Ground east component)^2
Ground heading = arctan(Ground north component / Ground east component)

Distance = 350 km
Time = Distance / Ground speed

By calculating these values, we can determine the ground speed, heading, and time required for the pilot to reach the airport.

This is not calculus, it is vector math. Work it as a Algebra II vector problem, breaking it into components. Most in the real world of navigation would do this graphically.