# Relative position

Hi this problem confuses me :

A sailor wants to travels due east at a velocity of 15km/h with respect to a coordinate system fixed to the ground.
The sailor must contend with the gulf stream, which moves north at 5 km/h. With which veolcity with respect to the water should the sailboat proceed under sail?

to try solve it I set :

Vbg= velocity of boat relative to ground.

Vwg= velocity of water relative to ground.

Vbw= velocity of boat relative to water.

now I wrote: Vbg= Vbw+Vwg but For me it does not fit.
What would fit is :
Vbw= Vbg+Vgw

here Vgw is not defined in the problem!

please can someone can help me?

Also, to find the angle θ of the boat, I am confused about what ( and where)put in the equation θ =tan-1(y/x)

Thank you

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Andrew Mason
Homework Helper
Hi this problem confuses me :

A sailor wants to travels due east at a velocity of 15km/h with respect to a coordinate system fixed to the ground.
The sailor must contend with the gulf stream, which moves north at 5 km/h. With which veolcity with respect to the water should the sailboat proceed under sail?

to try solve it I set :

Vbg= velocity of boat relative to ground.

Vwg= velocity of water relative to ground.

Vbw= velocity of boat relative to water.

now I wrote: Vbg= Vbw+Vwg but For me it does not fit.
What would fit is :
Vbw= Vbg+Vgw

here Vgw is not defined in the problem!

please can someone can help me?

Also, to find the angle θ of the boat, I am confused about what ( and where)put in the equation θ =tan-1(y/x)

Thank you

You know that this vector sum = 15 km/hr east. You also know that the water's velocity wrt land is 5 km/hr north. Work out the velocity of the boat relative to the water from that. $\theta$ is the angle of the boat's heading. The tangent of this angle is the north component/east component.