SOLUTION: To a person riding a bike with velocity (7 i + 3 j) km/h the wind seems to have velocity (9 i + 10 j) km/h. State the true velocity of the wind in i, j vector form. velocity (

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Question 998492: To a person riding a bike with velocity (7 i + 3 j) km/h the wind seems to have velocity (9 i + 10 j) km/h.
State the true velocity of the wind in i, j vector form.
velocity (km/h) =
What is the speed of the wind?
speed (km/h) =
Taking i as due East, what is the direction of the wind (in standard bearing notation) to the nearest degree?
bearing (°) ≈
THANK YOU

Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
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To a person riding a bike with velocity (7 i + 3 j) km/h the wind seems to have velocity (9 i + 10 j) km/h.
State the true velocity of the wind in i, j vector form.
velocity (km/h) =
What is the speed of the wind?
speed (km/h) =
Taking i as due East, what is the direction of the wind (in standard bearing notation) to the nearest degree?
bearing (°) ≈
-------------------------------------------------------------------------
To a person riding a bike with velocity  (r*i + s*j)    in a  still air  (at no wind)  the wind  seems  to have velocity  (-r*i, -s*j)  .  From here I make a conclusion that
    - if a person is riding a bike with velocity  (r*i + s*j)   relative to the earth surface and
    - if the wind is  (u*i + v*j)   relative to the earth surface,
then for the person the wind seems to have velocity  ((u-r)*i, (v-s)*j).

Thus we have the equations for the unknowns wind's velocity components (u*i, v*j)
u - 7 = 9       (for i-direction),   and
v - 3 = 10     (for j-direction).

It gives for the wind's velocity components   u = 7+9 = 16  for i-direction,   and   v = 3+10 = 13  for j-direction.

Hence.  the speed of the wind is    = = 20.6 .


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