The water in a river flows uniformly at a constant speed of 2.27 m/s between par

Question

The water in a river flows uniformly at a constant speed of 2.27 m/s between parallel banks 69.3 m apart. You are to deliver a package directly across the river, but you can swim only at 1.58 m/s.

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

(b) How far downstream will you be carried?
m

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

(d) How far downstream will you be carried?
m

Explanation / Answer

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 69.3 m = 1.58 m/s * t t = 43.86 seconds Then, the river will carry you downstream at 2.27 m/s for all 43.86 seconds, so the distance you will be carried downstream is: d = V * t d = 2.27 m/s * 43.86 seconds d = 99.56 m c.) To minimize the distance downstream the river will carry you, you need to swim at a 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 69.3 m = 1.58 * cos(45 degrees) * t t = 62.03 seconds Then, the river will carry you downstream at 2.27 m/s - 1.58 * sin(45 degrees) for all 62.03 seconds, so the distance you will be carried downstream is: d = V * t d = (2.27 - 1.58 * sin(45 degrees)) * 62.03 seconds d = 71.51 m

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.