# Relative motion and velocity

1. Oct 21, 2006

### PPonte

Problem:
A fisherman sets out upstream from Metaline Falls on the
Pend Oreille River in northwestern Washington State. His
small boat, powered by an outboard motor, travels at a
constant speed v in still water. The water flows at a lower
constant speed vw. He has traveled upstream for 2.00 km
when his ice chest falls out of the boat. He notices that
the chest is missing only after he has gone upstream for
another 15.0 minutes. At that point he turns around and
heads back downstream, all the time traveling at the same
speed relative to the water. He catches up with the floating
ice chest just as it is about to go over the falls at his
starting point. How fast is the river flowing? Solve this
problem in two ways. (a) First, use the Earth as a reference
frame. With respect to the Earth, the boat travels upstream
at speed v - vw and downstream at v + vw. (b) A
second much simpler and more elegant solution is obtained
by using the water as the reference frame. This approach
has important applications in many more complicated
problems; examples are calculating the motion of
rockets and satellites and analyzing the scattering of subatomic
particles from massive targets.​

I had no problem solving (a), my doubts arise when solving (b).

I desire to know if the following considerations for (b) are right:
• When the boat is travelling upstream his speed relative to the water reference frame is v + vw or simply v?
• When the boat is travelling downstream his velocity relative to the water reference frame is v - vw or simply v?
• The chest is motionless relative to the water reference frame.

Last edited by a moderator: Oct 21, 2006
2. Oct 21, 2006

### Hootenanny

Staff Emeritus
Hi there PPonte,

I've not been on the forums for a while, but it's nice to 'speak' to you again. All your considerations seem valid to me.

Edit: My apologies PPonte, I didn't see that your first two statements were actually questions. As SGT says, the velocity of the boat in the water's frame of reference is always v.

Last edited: Oct 21, 2006
3. Oct 21, 2006

### SGT

The velocity of the boat relative to the water is v, as is stated in the problem, no matter if the boat is travelling up or downstream.