Sailor's Wind Speed: 5.4mph East & 13.4mph SW/NE

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SUMMARY

The discussion focuses on calculating the true wind speed and direction affecting a sailboat sailing due east at 5.4 mph with wind appearing to blow from the southwest at 13.4 mph. The correct approach involves vector decomposition to find the resultant wind speed and direction. The initial calculation attempted by the user was incorrect due to a miscalculation in the vector components. The correct method requires using trigonometric functions to resolve the wind's components accurately.

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physics2hard
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A sailboat is sailing due east at 5.40 mph. The wind appears to blow from the southwest at 13.4 mph.

1. What is the true wind speed?
2.What is the true wind direction? ( south of west).
3.What is the true wind speed if the wind appears to blow from the northeast at 13.4 mph?
4.What is the true wind direction ( north of east) if the wind appears to blow from the northeast at 13.4 mph?

I tried solving the first question but did not get the correct answer. I know if you get the first question right it is easy to solve the second. Here's what I tried

sqrt ((13.4*sqrt (2)- 5.4)^2 + (13.4* sqrt(2))^2))= 23.29 mph but it wasn't right
this is Ax part this is Ay part

after finding the Ax and Ay just plug into equation:
theta=arctan(Ax/Ay)

PLEASE HELP ASAP NEED BY TONIGHT!
 
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Hi physics2hard! Welcome to PF! :smile:

(have a square-root: √ :smile:)
physics2hard said:
sqrt ((13.4*sqrt (2)- 5.4)^2 + (13.4* sqrt(2))^2))= 23.29 mph

erm … cos45º = 1/√2, isn't it? :wink:

(and check your minus sign)
 

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