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, we need to consider the effect of the wind.

First, let's break down the components of the plane's velocity.

1. The velocity of the plane relative to the air is the speed of the plane in still air, which is 200 km/h.
2. The velocity of the wind is 50.0 km/h in the east direction.

Since the wind is coming from the east, it will affect the plane's motion. The wind will add to or subtract from the plane's velocity depending on its direction.

Since the pilot keeps the plane pointed north (N), we can consider the north direction as the direction of the plane's motion relative to the ground.

Now, let's combine the components to determine the ground velocity of the plane:

1. The north component of the plane's velocity relative to the air is 200 km/h (since the pilot keeps the plane pointed north).
2. The east component of the wind velocity is -50.0 km/h (negative because the wind is coming from the east).

To find the ground velocity, we can use vector addition. The ground velocity is the vector sum of the plane's velocity relative to the air and the wind velocity.

Using vector addition, we can calculate the ground velocity:

Ground velocity = √(North component² + East component²)

Ground velocity = √((200 km/h)² + (-50.0 km/h)²)

Ground velocity = √(40,000 km²/h² + 2,500 km²/h²)

Ground velocity = √(42,500 km²/h²)

Ground velocity ≈ 206.2 km/h (rounded to one decimal place)

Therefore, the ground velocity of the plane, if the pilot keeps the plane pointed north (N), is approximately 206.2 km/h.