Upstream and Downstream one dimensional motion

[ashleyymariie]

Homework Statement

A fisherman sets out upstream on a river. 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. The fisherman has traveled upstream for 1.85 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 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 he returns to 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, such as calculating the motion of rockets and satellites and analyzing the scattering of subatomic particles from massive targets.


2. The attempt at a solution

First i set the displacement of the the fisherman while moving upstream equal to the displacement downstream.

1850+15(v-v(w))=(v+v(w))t(down)

But I am stuck once i get here because i do not know how long it takes him to get back down the river.

 

[PeterO]

Homework Statement

A fisherman sets out upstream on a river. 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. The fisherman has traveled upstream for 1.85 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 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 he returns to 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, such as calculating the motion of rockets and satellites and analyzing the scattering of subatomic particles from massive targets.


2. The attempt at a solution

First i set the displacement of the the fisherman while moving upstream equal to the displacement downstream.

1850+15(v-v(w))=(v+v(w))t(down)

But I am stuck once i get here because i do not know how long it takes him to get back down the river.

Try solving a similar question with just numbers to see if you can get a feel for the question. [It would be unfortunate if you just happened to guess the real answer].

EG: suppose the boat travels at 20 kph through the water, and the water flows at 6 kph, and the ice chest fell out 3.5 km up the river. [note! I don't expect he will "catch" the ice chest at the point where he set out in this case]