# Relative Velocities: Plane Displacement from City in 2h Time

• slpnsldr
In summary, the wind is blowing at 72km/h south relative to the earth and the plane is traveling at 320km/h (28 degrees south of west relative to the wind) directly above a city. Using the formula \vec{_{p}V_{E}}=\vec{_{p}V_{w}}+\vec{_{w}V_{E}}, the displacement from the city after 2 hours is 248km/h. However, the calculation for the new angle of the plane to the earth may require the use of the sine law, which may be difficult to explain without a diagram.

## Homework Statement

The wind is blowing at 72km/h south relative to the earth, and a plane is traveling 320km/h (28 degrees south of west relative to the wind) directly above a city. give displacement from the city in 2h time

## Homework Equations

Plane is P wind is W Earth is E

VPW=VPE+VWE

## The Attempt at a Solution

re arrange to find that
VPE=VPW-VWE
VPE=248km/h

The only thing I don't understand is how to determine the new angle of the plane to the earth...

Velocities are vectors. You cannot add or subtract them directly.

Hi slpnsldr. Your formula was incorrect. It should look like this
$$\vec{_{p}V_{E}}=\vec{_{p}V_{w}}+\vec{_{w}V_{E}}$$

Notice when you add these relative velocities, the subscript "w" cancel each other out. And that is the only trick to it.

ok, I've figured out my displacement.. but I am still unclear about how to find the planes new angle
somethign to do with the sine law?

slpnsldr said:
ok, I've figured out my displacement.. but I am still unclear about how to find the planes new angle
somethign to do with the sine law?

Oh, that might be hard to explain without a diagram. Maybe you need to include a diagram.

## 1. What is meant by "relative velocities"?

Relative velocities refer to the speed of an object in relation to another object. It takes into account the motion of both objects and calculates the difference in their velocities.

## 2. How is plane displacement measured from a city in 2 hours?

Plane displacement is measured by the distance traveled by the plane in relation to the city it departed from. In this case, the displacement would be measured in kilometers or miles.

## 3. What factors affect relative velocities?

The factors that affect relative velocities include the speeds of the two objects, the direction of their motion, and any external forces acting on them.

## 4. How is the time frame of 2 hours relevant to relative velocities?

The time frame of 2 hours is relevant because it is the amount of time that has passed since the plane departed from the city. It is used to calculate the displacement of the plane in relation to the city.

## 5. How is the concept of relative velocities useful in scientific research?

The concept of relative velocities is useful in scientific research for understanding the motion of objects and predicting their behaviors. It is also used in various fields such as physics, astronomy, and engineering to calculate velocities and trajectories of objects.