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While out camping, you are crossing a rather slow moving river; the banks are a distance Lapart; you enter the water and push off normal to the bank; you are doing back-stroke (so, you actually don't see where you are going) and you start swimming at an initial speed, vo, but you tire with a rate ao; when you arrive at the other bank, you realize that your landing spot is a distance d downstream from where you started (albeit on the opposite bank). a. Make a drawing of the situation and your frames of reference, one for the banks on for the water. b. Derive an expression for the velocity of the river as a function of L, d, vo and ao. c. How long are you in the water? What is your velocity (in each frame) with which you arrive at the opposite bank? d. What is the trajectory of your swim in each frame of reference? e. If L = 100 m, d = 20 m, vo = 2 m/s, and ao = 0.01 m/s², how fast does the river flow, and how long have you been in the water?

While out camping, you are crossing a rather slow moving river; the banks are a distance Lapart; you enter the water and push off normal to the bank; you are doing back-stroke (so, you actually don't see where you are going) and you start swimming at an initial speed, vo, but you tire with a rate ao; when you arrive at the other bank, you realize that your landing spot is a distance d downstream from where you started (albeit on the opposite bank). a. Make a drawing of the situation and your frames of reference, one for the banks on for the water. b. Derive an expression for the velocity of the river as a function of L, d, vo and ao. c. How long are you in the water? What is your velocity (in each frame) with which you arrive at the opposite bank? d. What is the trajectory of your swim in each frame of reference? e. If L = 100 m, d = 20 m, vo = 2 m/s, and ao = 0.01 m/s², how fast does the river flow, and how long have you been in the water?

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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2) While out camping, you are crossing a rather slow moving river; the banks are a distance \( L \) apart. You enter the water and push off normal to the bank; you are doing back-stroke (so, you actually don’t see where you are going) and you start swimming at an initial speed, \( v_0 \), but you tire with a rate \( a_0 \); when you arrive at the other bank, you realize that your landing spot is a distance \( d \) downstream from where you started (albeit on the opposite bank). a. Make a drawing of the situation and your frames of reference, one for the banks one for the water. b. Derive an expression for the velocity of the river as a function of \( L \), \( d \), \( v_0 \), and \( a_0 \). c. How long are you in the water? What is your velocity (in each frame) with which you arrive at the opposite bank? d. What is the trajectory of your swim in each frame of reference? e. If \( L = 100 \, \text{m} \), \( d = 20 \, \text{m} \), \( v_0 = 2 \, \text{m/s} \), and \( a_0 = 0.01 \, \text{m/s}^2 \), how fast does the river flow, and how long have you been in the water?
Transcribed Image Text:2) While out camping, you are crossing a rather slow moving river; the banks are a distance \( L \) apart. You enter the water and push off normal to the bank; you are doing back-stroke (so, you actually don’t see where you are going) and you start swimming at an initial speed, \( v_0 \), but you tire with a rate \( a_0 \); when you arrive at the other bank, you realize that your landing spot is a distance \( d \) downstream from where you started (albeit on the opposite bank). a. Make a drawing of the situation and your frames of reference, one for the banks one for the water. b. Derive an expression for the velocity of the river as a function of \( L \), \( d \), \( v_0 \), and \( a_0 \). c. How long are you in the water? What is your velocity (in each frame) with which you arrive at the opposite bank? d. What is the trajectory of your swim in each frame of reference? e. If \( L = 100 \, \text{m} \), \( d = 20 \, \text{m} \), \( v_0 = 2 \, \text{m/s} \), and \( a_0 = 0.01 \, \text{m/s}^2 \), how fast does the river flow, and how long have you been in the water?
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