A small plane can travel at 200 km/h in still air. If a 50.0 km/h wind is coming from the east, determine the ground velocity of the plane if the pilot keeps the plane pointed [N].
To determine the ground velocity of the plane when it is pointed north, we need to consider the effect of the wind.
The plane's speed in still air is given as 200 km/h. This means that when there is no wind, the plane can travel at a speed of 200 km/h relative to the air.
Now, let's consider the wind. The wind is blowing from the east at a speed of 50.0 km/h. Since the wind is directly opposing the direction the plane is traveling when it is pointing north, the wind will act as a headwind.
To find the ground velocity, we need to add or subtract the wind speed from the speed of the plane in still air, depending on the direction of the wind relative to the direction the plane is pointing.
In this case, the wind is opposing the plane's direction, so we subtract the wind speed from the plane's speed in still air:
Ground velocity = Speed of the plane in still air - Wind speed
= 200 km/h - 50.0 km/h
= 150.0 km/h
Therefore, the ground velocity of the plane when it is pointed north will be 150.0 km/h.
Vp + Vw = 200kn/h[90o]
Vp + (-50) = 200i
Vp = 50 + 200i = 206.2km/h[76o]