Relative Velocity in 2 Dimensions

[Neen87]

Homework Statement

Suppose the river is moving east at 5 km/h and the boat is traveling 45 degrees south of east with respect to earth. Find (a) the speed of the boat with respect to Earth and (b) the speed of the boat with respect to the river if the boat's heading in the water is 60 degrees south of east. You will have to solve 2 equations and two unknowns.
ANSWERS: (a) 16.7 km/h (b) 13.7 km/h

Homework Equations

V_BR = V_BE - V_RE

V_0x = V₀ cos theta₀
V_0y = V₀ sin theta₀

The Attempt at a Solution

The problem preceding this one has the boat traveling at 10 km/h relative to the river. I am assuming here that the boat is still traveling at this speed, since none other is given.

V_BR: x component = 10 cos theta; y component = -10 sin theta
V_BE: x component = v₀ cos (45); y component = v₀ sin (-45)
V_RE: x component = 5 km/h; y component = 0

This question was asked on a thread several years ago; however, the solution was incorrect. Any help would be appreciated! Thank you :)

 

[gneill]

The speed of the boat with respect to the river is one of the things you're supposed to find.

I think you have to proceed on the basis that you're given two direction angles, 45° and 60° with respect to the Earth and river respectively, both measured south of east, and you have the speed of the eastward flow of the river which will relate those two angles.

I would write expressions for the angles using the velocity components of the boat with respect to the river, then solve.