# Relative Velocities

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• August 21st 2009, 07:03 AM
Harry1W
Relative Velocities
The question reads:

"A glider is moving with a velocity $v = (40, 30, 10)$ relative to the air and is blown by the wind which has velocity relative to the earth of $w = (5, -10, 0)$. Find the velocity of the glider relative to the earth."

My argument goes that as the velocity of the wind relative to the earth increases, and the velocity of the glider relative to the air, increase, so does the velocity of the glider relative to earth. So if we let $v_E$ represent the velocity of the glider relative to the earth,

$v_E = v + w$.

Therefore, in this case the velocity of the glider relative to the earth,

$v_E = (40, 30, 10) + (5, -10, 0) = (45, 20, 10)$

However, the answer booklet has the expression for $v_E$ as follows:

$v_E = v - w$

giving $v_E = (35, 40, 10)$ which I suppose must be the right answer. Could somebody explain this result to me? Thank you.
• August 21st 2009, 02:45 PM
skeeter
Quote:

Originally Posted by Harry1W
The question reads:

"A glider is moving with a velocity $v = (40, 30, 10)$ relative to the air and is blown by the wind which has velocity relative to the earth of $w = (5, -10, 0)$. Find the velocity of the glider relative to the earth."

My argument goes that as the velocity of the wind relative to the earth increases, and the velocity of the glider relative to the air, increase, so does the velocity of the glider relative to earth. So if we let $v_E$ represent the velocity of the glider relative to the earth,

$v_E = v + w$.

Therefore, in this case the velocity of the glider relative to the earth,

$v_E = (40, 30, 10) + (5, -10, 0) = (45, 20, 10)$

However, the answer booklet has the expression for $v_E$ as follows:

$v_E = v - w$

giving $v_E = (35, 40, 10)$ which I suppose must be the right answer. Could somebody explain this result to me? Thank you.

I agree with you ... (air vector) + (wind vector) = ground vector

the answer booklet is in error, imho.
• August 22nd 2009, 06:46 AM
Grandad
Hello Harry1W
Quote:

Originally Posted by Harry1W
The question reads:

"A glider is moving with a velocity $v = (40, 30, 10)$ relative to the air and is blown by the wind which has velocity relative to the earth of $w = (5, -10, 0)$. Find the velocity of the glider relative to the earth."

My argument goes that as the velocity of the wind relative to the earth increases, and the velocity of the glider relative to the air, increase, so does the velocity of the glider relative to earth. So if we let $v_E$ represent the velocity of the glider relative to the earth,

$v_E = v + w$.

Therefore, in this case the velocity of the glider relative to the earth,

$v_E = (40, 30, 10) + (5, -10, 0) = (45, 20, 10)$

However, the answer booklet has the expression for $v_E$ as follows:

$v_E = v - w$

giving $v_E = (35, 40, 10)$ which I suppose must be the right answer. Could somebody explain this result to me? Thank you.

You need to check on the definition of 'wind velocity'. Sometimes (perversely!) it's given as the direction from which the wind blows. For example, a north-easterly is a wind that blows from the N-E; i.e towards the South-West.

This would indeed make the velocity of the glider relative to the earth $v - w$.

Grandad
• August 22nd 2009, 06:48 AM
skeeter
Quote:

Originally Posted by Grandad
Hello Harry1WYou need to check on the definition of 'wind velocity'. Sometimes (perversely!) it's given as the direction from which the wind blows. For example, a north-easterly is a wind that blows from the N-E; i.e towards the South-West.

This would indeed make the velocity of the glider relative to the earth $v - w$.

Grandad

I thought about that also, but dismissed it since the wind was given in proper vector notation.