# Vector based problem

#### I<3Champlin

Okay I am having a total brain freeze on this physics review I am doing. The problem is as follows:

A sailboat is sailing due east at 7.8 mph. The wind appears to blow from the southwest at 12.9 mph.
(a) What are the true wind speed and direction? Speed in m/s Direction ° (counter-clockwise from east)
(b) What are the true wind speed and direction if the wind appears to blow from the northeast at 12.9 mph? Speed in m/s Direction ° (counter-clockwise from east)

Any help would be great!

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#### Parvez

PHF Hall of Honor
See the attachment. Vb is the velocity of boat, Vwb is the velocity of wind as seen by boat and Vw is the actual (wrt earth ) velocity of the wind.Since wind is comming from SW hence it is derected towatds NE. Now-
Vwb = Vw - Vb ( by the definition of relative velocity )
Vw = Vwb + Vb ( bold represents vectors )
Now use the law of vector addition to find Vb from the eq
Vw = sqrt{Vwb^2 + Vb^2 + 2*Vwb*Vb*cos45}

The angle @ that Vw makes with East(also the direction of Vb) can be found from
[email protected] = Vwb*[email protected]/{Vb+Vwb*[email protected]}

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