Motion in a Plane, Vector Addition/Subtraction

[TheModernAge]

Homework Statement

Snoopy is flying his plane, the Sopwith Camel, in search of the Red Baron. He flies with a constant speed of 120 km/h relative to air, and makes instantaneous turns when necessary. He follows a perfectly square path on the ground, using north - south and east - west roads as a guide for each of the 60 km sides. On a day when there is a steady 60 km/h wind blowing diagonally across the square (southwest wind), how long does the trip take?

Homework Equations

Relative Motion
V-speed, P-Plane, A-Air, G-Ground
_PV_G = _PV_A + _AV_G

Cosine Law

The Attempt at a Solution

My assumption on the problem is that the airspeed of 120 km/h must have an added components of 60 km/h (NE) to counteract it so that the resultant will have its course on the correct path 60 km North. This is done for each side.
I have drawn out my vectors in the attached image.
Using cosine law I can find the new airspeed, but I don't know what to do after.
Please Help and Thank You

 

[PeterO]

Homework Statement

Snoopy is flying his plane, the Sopwith Camel, in search of the Red Baron. He flies with a constant speed of 120 km/h relative to air, and makes instantaneous turns when necessary. He follows a perfectly square path on the ground, using north - south and east - west roads as a guide for each of the 60 km sides. On a day when there is a steady 60 km/h wind blowing diagonally across the square (southwest wind), how long does the trip take?

Homework Equations

Relative Motion
V-speed, P-Plane, A-Air, G-Ground
_PV_G = _PV_A + _AV_G

Cosine Law

The Attempt at a Solution

My assumption on the problem is that the airspeed of 120 km/h must have an added components of 60 km/h (NE) to counteract it so that the resultant will have its course on the correct path 60 km North. This is done for each side.
I have drawn out my vectors in the attached image.
Using cosine law I can find the new airspeed, but I don't know what to do after.
Please Help and Thank You

Your diagram will find a new ground speed if Snoopy points the plane due North, then "side-slips" his way across the landscape.
Snoopy is to maintain a ground speed of due North, so on the first leg will be pointing somewhat West of North.

The wind speed adds a constant North and East component to any velocity the plane has relative to the air.
To fly in a specific N, S, E or W direction, the velocity of the plane must have a component to cancel out the "unwanted" component of the wind.

For example, suppose a different wind had a North component of 20 km/h, and an East component of 20 km/h.

To fly North, the 120km/h of the plane would have to have a westerly component of 20 km/h to balance the wind and achieve a due North heading.

PS. Wouldn't it be weird if the problem could be worked out this simply:
If there was no wind, Snoopy merely points N, E, S then W, and flies for 60km each time, to cover the square. That would take 2 hours.
If he did that with the wind blowing, he would actually end up 120 km NE of where he started. It would take 2 hours to return to his starting point [he would be flying into a head wind so only gaining 60 k each hour]. So the whole trip would take 4 hours.