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

[physics2hard]

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!

 

[tiny-tim]

Welcome to PF!

Hi physics2hard! Welcome to PF!

(have a square-root: √ )

sqrt ((13.4*sqrt (2)- 5.4)^2 + (13.4* sqrt(2))^2))= 23.29 mph

erm … cos45º = 1/√2, isn't it?

(and check your minus sign)

 

[baba89]

1. The true wind speed can be calculated using the Pythagorean theorem: √(5.4^2 + 13.4^2) = 14.35 mph. This is the magnitude of the wind speed, regardless of direction.

2. To find the true wind direction, we can use the inverse tangent function (arctan) to find the angle between the east direction and the direction of the wind. This can be calculated as: arctan(13.4/5.4) = 68.8 degrees. Therefore, the true wind direction is 68.8 degrees south of west.

3. If the wind appears to blow from the northeast at 13.4 mph, we can use the same method as above to find the true wind speed: √(5.4^2 + 13.4^2) = 14.35 mph. This means that the true wind speed remains the same regardless of the direction it appears to be blowing from.

4. To find the true wind direction when the wind appears to blow from the northeast, we can use the same method as above, but this time the angle will be in the opposite direction: arctan(5.4/13.4) = 21.2 degrees. Therefore, the true wind direction would be 21.2 degrees north of east.