Re: Solution to a problem!!

[Ludwik Kowalski <kowalskiL@Mail.Montclair.edu>]

The problem is quoted at the end.
Assuming the river flows from left to right the boy must aim the
boat at a point A located x km to the left from the girl. To minimize
time he would plan to land at a point B on the right of the girl (not
exactly at her location because he runs faster than he rows). The rest
is just to compose the expression for the total time t=t1+t2 (rowing
and running) in terms of the independent variable x (and other
given parameters). Calculate the derivative of t with respect to x and
equate it to zero. This will give you the best possible x. And the angle
D you want is given by tan(D)=x/w, where w is the width of the river.

To solve the problem without calculus (as far as I can tell) would
be to use the "brute numerical force".  Calculate t for several x
numerically, plot the curve and locate its minimum.
                                                    Ludwik Kowalski
James Harris wrote:

> Dear Physics People,
>
> I gave the following problem as an extra credit exercise on a test for my
> Honors physics.
> What would you say the solution was? I believe it is from Tipler Physics. I
> don't have an answer key for the book so I am not sure. A couple of kids got
> into a pretty good debate (until the soccer coach arrived and chewed them
> out) over what the solution is or was.
> Jim
> jharris@monad.net or jharris@newpisgah.keene.edu
> Teacher: Monadnock Regional High School
> Adjunct Faculty: Keene State College, Chemistry Department
>
> EXTRA CREDIT   Jack/Jill is strolling along the bank of a river 1 km wide
> when the most beautiful/handsome girl/boy he/she has ever seen materializes
> on the shore directly opposite him/her (perhaps she/he was beamed down?).
> Fearing that she/he will disappear before he/she has a chance to establish
> face-to-face communication, he/she quickly devises a plan to reach the
> opposite shore in the shortest possible time. In the wildest of
> coincidences, there is a rowboat beached on the shore right in front of
> him/her. Jack/Jill is ecstatic, because it so happens that he/she's an
> expert oarsperson. (He/she rows on the crew for an ivy league school.)
> He/she knows that he/she can row at a speed of 6 km/h in still water, and
> he/she estimates--as he/she sprints for the boat at 10 km/h--that the river
> current has a speed of 4 km/h. Now, besides being an athlete and an
> excellent judge of river velocities, Jack/Jill is also an accomplished
> physics student. During his/her sprint to the boat, he/she computes the path
> he/she must take from his/her side of the river to reach the girl/boy on the
> opposite side in the shortest possible time. In general, his/her path
> includes a diagonal trip across the river followed by a sprint along the
> opposite shore to reach his/her goal. (Note that Jack/Jill has a standard
> sprinting speed of 10 km/h.) Assuming that Jack/Jill did the physics
> correctly, in what direction did he/she head the boat and how long did it
> take him/her to establish first contact?