Solving Relative Position Problem: Velocity of Boat w.r.t Water

[brad sue]

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 :

V_bg= velocity of boat relative to ground.

V_wg= velocity of water relative to ground.

V_bw= velocity of boat relative to water.

now I wrote: V_bg= V_bw+V_wg but For me it does not fit.
What would fit is :
V_bw= V_bg+V_gw

here V_gw 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

brad

 

[Andrew Mason]

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 :

V_bg= velocity of boat relative to ground.

V_wg= velocity of water relative to ground.

V_bw= velocity of boat relative to water.

now I wrote: V_bg= V_bw+V_wg but For me it does not fit.
What would fit is :
V_bw= V_bg+V_gw

here V_gw 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

brad

The vector sum of the boat's velocity relative to the water and the water's velocity relative to the land gives you the boat's velocity relative to the land.

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.

AM