# Relative Motion - Airplane Problem

• harujina
In summary, the problem involves finding the velocity of an airplane relative to the ground when given its velocity relative to air and the wind velocity. Using the equation pVg = aVg + pVa and given pVa = 325km/h [S30W] and aVg = 80km/h [W], the velocity of the plane relative to the ground is unknown. To solve for pVg, the vectors must be divided into components. The direction of pVg is unknown and cannot be assumed without further information.
harujina

## Homework Statement

An airplane has a velocity 325km/h relative to the air. It is going in a direction [S30W]. There is a wind velocity of 80km/h[W]. What is the velocity of the plane relative to the ground?

## Homework Equations

aVg + pVa = pVg
(velocity of air relative to ground + velocity of plane relative to air = velocity of plane relative to ground)

## The Attempt at a Solution

pVa = 325km/h and aVg = 80km/h [W] and pVg = ? [S30W]

correct?
i know pVg^2 = aVg^2 + pVa^2
but, I'm not getting the number I'm supposed to?

The problem does not state specifically that the vectors form a 90 degree triangle. So you cannot assume that.

You could divide pVa into components.

Can you possibly attach a diagram showing the vectors?

harujina said:
pVa = 325km/h and aVg = 80km/h [W] and pVg = ? [S30W]
Where do you get the direction from? I read it as pVa = 325km/h [S30W] and the direction of pVg is unknown. See if that gives the desired answer.

## 1. What is relative motion in the context of an airplane?

Relative motion in the context of an airplane refers to the movement of the airplane in relation to a fixed point on the ground or another object in the air. It takes into account the speed and direction of both the airplane and the reference point to determine the airplane's position and movement.

## 2. How does wind affect an airplane's relative motion?

Wind can significantly affect an airplane's relative motion by changing its speed and direction. If the wind is blowing in the same direction as the airplane's movement, it can increase the airplane's speed. However, if the wind is blowing in the opposite direction, it can decrease the airplane's speed and cause it to drift off course.

## 3. What is the difference between airspeed and groundspeed in relative motion?

Airspeed is the speed of an airplane relative to the air around it, while groundspeed is the speed of the airplane relative to the ground. Airspeed takes into account the effects of wind, while groundspeed does not. Therefore, an airplane's groundspeed may be different from its airspeed depending on the direction and strength of the wind.

## 4. How do you calculate the heading of an airplane in relative motion?

The heading of an airplane in relative motion can be calculated using a compass or by using mathematical formulas that take into account the airplane's airspeed, wind speed, and wind direction. The heading is the direction in which the airplane is pointing and is typically expressed in degrees, with 0 degrees being north and 180 degrees being south.

## 5. What role does the pilot play in controlling relative motion of an airplane?

The pilot plays a crucial role in controlling the relative motion of an airplane. He or she is responsible for adjusting the airplane's speed, direction, and altitude to ensure a safe and efficient flight. The pilot must also take into account the effects of wind and make necessary adjustments to maintain the desired heading and airspeed.

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