Relative Velocities with angles

[Jtappan]

Homework Statement

A dolphin wants to swim directly back to its home bay, which is 0.79 km due west. It can swim at a speed of 4.14 m/s relative to the water, but a uniform water current flows with speed 2.93 m/s in the southeast direction.

(a) What direction should the dolphin head?
_______° N of W
(b) How long does it take the dolphin to swim the 0.79-km distance home?
________min

The Attempt at a Solution

First I have been trying to find all of my variables in both directions. The angle should be 45 degrees for the 2.93m/s in the south east directions, I am pretty sure. Then I am just completely lost after that. If it is a 45 degree angle then you do 2.93sin45 and get 2.07 roughly. This is where it loses me because there are two different velocities for the Dolphin relative to the water.

 

[learningphysics]

Let theta be the angle of the dolphin's velocity from the positive east axis...

So the dolphin goes 4.41cos(theta) in the horizontal direction...

He goes 4.41sin(theta) in the vertical direction.

What is the horizontal and vertical component of the water...

What can you say about the sum of the vertical component of the water + the vertical component of the dolphin's velocity? That should let you get theta... also note, theta should be bigger than 90 degrees... because the dolphin needs to go west...