# Relative Velocities

1. Sep 20, 2007

### Jtappan

1. The problem statement, all variables and given/known data

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

2. Relevant equations

kinematics equations

3. The attempt at a solution

2. Sep 20, 2007

### FedEx

Welcome to the forums.

This sum has to be done by vectors or relative velocity.

And as you are new to the forums i would like to remind you that every homework thread should also carry the attempts made by the person in solving that problem. We are here to help you in your homework not to do your homework.

3. Sep 20, 2007

### Jtappan

Sorry

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, im 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.

4. Sep 21, 2007

### FedEx

Be frank

Try do it with relative velocities.Here

$$\vec{v}_{dg}$$ = $$\vec{v}_{dr}$$ - $$\vec{v}_{gr}$$

Hence $$\vec{v}_{dg}$$ = $$\vec{v}_{dr}$$ + $$\vec{v}_{rg}$$

Now here $$\vec{v}_{dg}$$ is the velocity of the dolphin wrt the ground.

$$\vec{v}_{dr}$$ is the velocity of the dolphin wrt the river.

$$\vec{v}_{rg}$$ is the velocity of the river wrt the ground.

5. Sep 21, 2007

### worldisonline

A question

i have a question :) can u solve it :)

find the equation of circle which passes through the point (-2,-4) and has the same center as the circle whos equation is x^2+y^2-4x-6y-23=0 ??

6. Sep 21, 2007

### learningphysics

worldisonline, you should start your own thread in the Precalculus section of the Homework forums. Also, show us how you approached the problem, and where you got stuck.

7. Sep 21, 2007

### FedEx

I think that you are a bit weak at relative velocities.

Lets start it again, I have inserted the diagram have a look at it.Here first consider the x components and you ewill that

Vrgcos(45) + Vdrcos(90) = Vdgcos(A+45)
Hence Vrgcos45=Vdgcos(A+45)

Now consider the y components

Vrgsin45+Vdrsin90 = Vdgsin(45+A)

Vrg=2.93 and Vdr=4.14 m/s.

Now solve the two.

Sorry learning and doc but i had to give the whole method. I was getting PM from the OP and belive me he was completely at sea.

8. Sep 21, 2007

### learningphysics

No prob Fedex. But I'm confused by your method... Why are you using 90 degrees and A+45?

9. Sep 21, 2007

### FedEx

Forgot to attach the diagram.Sorry.

#### Attached Files:

• ###### The figure.doc
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10. Sep 21, 2007

### andrevdh

The resultant motion of the dolphin needs to be to the west, lets call it $$\vec{v_w}$$. This motion is the combined motion of the current, lets call it $$\vec{v_c}$$, and the direction in which the dolphin needs to swim, lets call it $$\vec{v_d}$$. These three vectors will form a closed triangle with the resultant of the other two being $$\vec{v_w}$$.

#### Attached Files:

• ###### dolphin.gif
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Last edited: Sep 21, 2007