Please include the steps on how you came to the conclusion of your answer. The h
ID: 251865 • Letter: P
Question
Please include the steps on how you came to the conclusion of your answer. The help is much appreciated
Name: Unit 3- Challenging Problem Against the Grain You are on the west bank of a river which flows due south and want to swim to the east bank. You have told your friends to meet you on the east bank directly opposite your starting point. Before starting out, you realize that, since the river is flowing swiftly at a speed of 12 ft/s and since your fastest swimming speed in still water is only 5 ft/s, you will inevitably be carried downstream. Nevertheless, you want to minimize the effort expended by your friends in walking downstream to meet you. Your guide book to the region tells you that the width of the river is 300 ft. After a quick calculation you call your friends on your cellular phone and tell them to start walking to new meeting point. How far downstream of the original meeting point should you tell them to walk?Explanation / Answer
5feet/sec times
cos cos across,
and 5 ft/sec times sin in the upstream direction. The last term is just 12 feet/sec downsteam.
The net velocity is vx= 5cos across
and v y= 12 - 5sin downstream the time to get across is 300 feet/ v x, ort = d / v x = 300 ft /
5(ft/sec) cos the distance D we go downstream in that time is
D = t vy = ( 300 ft / 5(ft/sec) cos )(12ft/sec-5(ft/sec)sin) which must be minimized as a function of the heading taking the derivative analytically and setting it to zero.
The answer is =arcsin(5/12) = 24.6 °.
This may be substituted into the above D() to find the minimum D
. D can be minimized by plotting D() and picking out the minimum that way
.The answer is 655 feet.
The time to cross was 66 seconds This minimizes the time to cross,
giving t = 60 seconds. But we land 720 = 12*60 feet downstream