# Vehicle moving along a path tangent to the Earth surface

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In summary, the conversation discusses the confusion between "with respect to the path" and "with respect to the earth" and how the path being attached to the Earth affects the vehicle's acceleration. The goal is to determine the velocity of the vehicle relative to the Earth so that it has zero acceleration in the vertical direction.
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Homework Statement
A vehicle moves along a path perfectly tangent to the earth surface in the Equator. The path doesn't have any curvature in the vertical plane. What velocity should have the vehicle with respect to the path so that its vertical acceleration component is zero? (consider that the Earth centre is not accelerated). Then, how would your previous answer change if the vehicle moves along a path that has the same curvature that the Earth?
Relevant Equations
##\vec a=\vec a_B + \vec{\dot \omega} \times \vec r + \vec \omega \times (\vec \omega \times \vec r) + 2. (\vec \omega \times \vec v_{rel}) + \vec a_{rel}##
Here I have some problems. I get confused when it says"with respect to the path", is it different from "with respect to the earth"? Because the path is on the Earth. Then, the vehicle is not accelerated in the vertical direction because it moves along the path, is it?

The path is attached to the Earth and rotates with the earth. You need to determine the magnitude and direction of the velocity of the vehicle relative to the Earth so that, relative to the non-rotating inertial frame, the car has zero acceleration in the vertical direction (zero acceleration in the y-direction at the instant shown in the figure below).

## 1. What is the path of a vehicle moving along a path tangent to the Earth surface?

The path of a vehicle moving along a path tangent to the Earth surface is called a tangential trajectory. This means that the vehicle is moving along a path that is parallel to the Earth's surface at all times.

## 2. How does the Earth's curvature affect the path of a vehicle moving tangent to its surface?

The Earth's curvature plays a crucial role in the path of a vehicle moving tangent to its surface. Because the Earth is round, the vehicle must constantly adjust its direction to maintain a tangent path. This is known as the vehicle's tangential acceleration.

## 3. What forces are acting on a vehicle moving along a path tangent to the Earth surface?

There are several forces acting on a vehicle moving along a path tangent to the Earth surface. These include the vehicle's engine force, which propels the vehicle forward, and the Earth's gravitational force, which pulls the vehicle towards the center of the Earth. Other factors, such as air resistance and friction, may also affect the vehicle's movement.

## 4. Can a vehicle maintain a tangent path without any external forces?

No, a vehicle cannot maintain a tangent path without any external forces. In order to overcome the Earth's gravitational pull and maintain a constant tangential velocity, the vehicle requires the engine force to counteract these external forces.

## 5. How does the speed of a vehicle affect its tangential trajectory?

The speed of a vehicle has a direct impact on its tangential trajectory. The faster the vehicle is moving, the more difficult it is to maintain a tangent path due to the increased forces acting on the vehicle. However, with proper adjustments to the vehicle's engine force, a constant tangential velocity can be maintained at any speed.

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