How can the dolphin reach its home bay while swimming against a river current?

[Snoop06]

Homework Statement

A dolphin wants to swim directly back to its home bay, which is 0.77 km due west. It can swim at a speed of 4.49 m/s relative to the water, but a uniform water current flows with speed 2.75 m/s in the southeast direction.

(a) What direction should the dolphin head?

(degrees) N of W

(b) How long does it take the dolphin to swim the 0.77-km distance home?

(min)

Homework Equations

The Attempt at a Solution

I have been trying this for a while now, and have just been getting more and more frustrated. I must be missing something simple but I can't figure it out. I tried assuming that "southeast" meant directly, ie 45*, with no luck. I also tried to somehow get two different equations with the angle in them to set equal to each other but couldn't find a way to do that either. Any help is appreciated.

Thanks,
Justin

 

[learningphysics]

There are 2 ways to solve this (and all these types of problems)... graphically where you solve using the geometry of a triangle... or using components...

Using components... if the angle is theta of the velocity of the dolphin relative to water... the dolphin's east/west velocity is... 4.49 cos(theta). the north south component is 4.49sin(theta)

what is the east/west component of the river's velocity (yes, it is 45 degrees)... what is the north south component?

What can you tell about the sum of the dolphin's north south velocity, and the river's north/south velocity?

 

[Snoop06]

There are 2 ways to solve this (and all these types of problems)... graphically where you solve using the geometry of a triangle... or using components...

Using components... if the angle is theta of the velocity of the dolphin relative to water... the dolphin's east/west velocity is... 4.49 cos(theta). the north south component is 4.49sin(theta)

what is the east/west component of the river's velocity (yes, it is 45 degrees)... what is the north south component?

What can you tell about the sum of the dolphin's north south velocity, and the river's north/south velocity?

Ah I wasn't relating the north/south velocity of the current to the north/south velocity of the dolphin. That makes it all work out with the 45* angle. Thanks for the help :)