# The time it takes this thing to travel across 3 points

• Mewtwo
In summary, the problem involves finding the shortest time for a thing to travel from point P to point A on land, and then from point A to point Q in water. The given speeds for land and water are 25m/s and 20m/s, respectively. The distance between P and A is 50m. The time for this route is given by T(theta)=pi-20+5sin(theta/2).
Mewtwo
Hey! I have a problem that I have no clue how to solve. So I was hoping you guys could help me. I'm not from an English speaking country so I apologize.

## Homework Statement

A thing is made to travel in water and on land. In water it travels with 20 m/s speed but on land with 25m/s speed. The thing starts at point P on the edge of a pond with radius 50m.

(I drew this picture in paint and what I forgot to include is that the curved line from P to A and the straight line from A to Q are a little bit darker then the other lines, so it seems to me that the thing travels on land from P to A but in water from A to Q).

(a) Show that the time it takes the thing to travel from P to A to Q is:
T(theta)=pi-20+5sin(theta/2)

(b) Give a description of the route that takes the shortest time for the thing to travel.

Mewtwo said:
(a) Show that the time it takes the thing to travel from P to A to Q is:
T(theta)=pi-20+5sin(theta/2)

I think you mean ##T(\theta)=\pi - 2\theta + 5\sin{\frac \theta 2}##. But nobody here is going to work it for you. Show us what you have for part (a.)

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## 1. How is the time it takes for an object to travel across 3 points calculated?

The time it takes for an object to travel across 3 points is calculated using the formula: time = distance/velocity. This means that the time is directly proportional to the distance and inversely proportional to the velocity. The larger the distance, the longer the time, while the larger the velocity, the shorter the time.

## 2. What factors affect the time it takes for an object to travel across 3 points?

The time it takes for an object to travel across 3 points is affected by various factors such as the distance between the points, the speed or velocity of the object, and any external forces acting on the object. Other factors may include the shape and weight of the object, as well as the medium through which it is traveling.

## 3. Can the time it takes for an object to travel across 3 points be predicted accurately?

Yes, the time it takes for an object to travel across 3 points can be predicted accurately if all the necessary factors are known and taken into consideration. However, there may be slight variations due to external factors or unforeseen circumstances.

## 4. How does the time it takes for an object to travel across 3 points differ in different mediums?

The time it takes for an object to travel across 3 points can differ in different mediums due to variations in factors such as density, viscosity, and other properties of the medium. For example, an object may travel faster in air compared to water, as air has a lower density and less resistance.

## 5. Is the time it takes for an object to travel across 3 points affected by the curvature of the surface it is traveling on?

Yes, the time it takes for an object to travel across 3 points can be affected by the curvature of the surface it is traveling on. This is because the distance between the points may change due to the curvature, which will in turn affect the overall time taken. This is particularly evident in curved paths such as orbits or trajectories.

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