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].

See previous post: Mon,4-21-14,2:27 PM.

To determine the ground velocity of the plane when it is pointed north, we need to consider the effect of the wind.

First, let's break down the plane's velocity into its horizontal and vertical components. Since the plane is flying north, its vertical component is the speed of the plane itself, which is 200 km/h.

Now, let's calculate the horizontal component. Since there is a 50.0 km/h wind coming from the east, it will affect the plane's horizontal movement. When a plane is flying in a crosswind, the wind creates a perpendicular force that affects the plane's speed and direction.

Since the plane is flying north and the wind is coming from the east, the wind creates a force that pushes the plane towards the west. This is known as the crosswind component.

To find the crosswind component, we can use trigonometry. The crosswind component is the product of the wind speed and the cosine of the angle between the wind direction and the plane’s direction. In this case, since the plane is pointing north, the angle between the wind and the plane's direction is 90 degrees.

So, the crosswind component is given by: crosswind component = wind speed * cos(90°) = 50.0 km/h * cos(90°) = 0 km/h.

Since the crosswind component is zero, it means the wind has no effect on the plane's northward movement. Therefore, the ground velocity of the plane when it is pointed north is equal to its vertical component, which is 200 km/h.

Therefore, the ground velocity of the plane when it is pointed north, with a 50.0 km/h wind coming from the east, is 200 km/h.