Question

The water in a river flows uniformly at a constant speed of 2.93 m/s between parallel banks 90.3 m apart. You are to deliver a package directly across the river, but you can swim only at 1.25 m/s.

(a) If you choose to minimize the time you spend in the water, in what direction should you head?

(b) How far downstream will you be carried?

(c) If you choose to minimize the distance downstream that the river carries you, in what direction should you head?

(d) How far downstream will you be carried?

Answer 1

a) To spend the least amount of time in the water, you should head directly toward the other bank. (90 degrees from the bank of the stream). This makes all of your speed used toward crossing the bank, and gives you the shortest time in the water.

b) To find the distance downstream you will be carried, you need to find the time in the water:

d = V * t
90.3 m = 1.25 m/s * t
t = 72.24 seconds

Then, the river will carry you downstream at 2.93 m/s for all 72.24 seconds, so the distance you will be carried downstream is:

d = V * t
d = 2.93 m/s * 72.24 seconds
d = 211.66 m

c) To minimize the distance downstream the river will carry you, you need to swim at a 135 (90 + 45) degree angle toward the stream.

d) To find the distance downstream you will be carried, you need to find the time in the water:

d = V * t
90.3 m = 1.25 * cos(45 degrees) * t
t = 102.16 seconds

Then, the river will carry you downstream at 2.93 m/s - 1.25 * sin(45 degrees) for all 102.16 seconds, so the distance you will be carried downstream is:

d = V * t
d = (2.93 - 1.25 * sin(45 degrees)) * 102.16 seconds
d = 209.03 m