# Math Help - Relative Velocities

1. ## Relative Velocities

"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.

2. Originally Posted by Harry1W

"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.

3. Hello Harry1W
Originally Posted by Harry1W

"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 $v - w$.

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