What is the Missing Information in Determining Wind Speed and Direction?

[PhysicsMark]

Homework Statement

A sailboat is heading due east at 8 mph. The wind appears to blow from the south west (toward the north east – that is 45 degrees north of east) as observed from the sailboat. What is the speed and direction of the wind as observed from the ground?

Homework Equations

The Attempt at a Solution

I drew a vector due east with magnitude 8. From the head of the vector I drew another vector at a 45 degree angle. Before I can solve the triangle, don't I need to know the magnitude of the wind?

 

[rl.bhat]

Observer on the sail boat feels that he is moving in the direction of wind. This direction is the resultant of his speed due east and wind speed due ...?

 

[PhysicsMark]

North?

 

[ideasrule]

Observer on the sail boat feels that he is moving in the direction of wind. This direction is the resultant of his speed due east and wind speed due ...?

Not necessarily. Nothing in the problem says the wind's eastward component is due only to the boat's motion. For all we know, the eastward component might be one 1 000 000 miles per hour. A person on the shore would see the wind's northward component as 1 000 000 mph and its eastward component as 1 000 008, for a total speed of roughly 1.4 million mph.

Alternatively, both components could be 1 mph from the boat's reference frame. The shore would think the wind is blowing 1 mph north and 7 mph west, for a total of 7 mph.

Conclusion: yes, this problem is missing info. There's no way you can determine either the speed or the velocity of the wind from the reference frame of the ground.