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Omar swims across a river at a velocity of 2.50 m/s [30 o N of E] with respect to the water. The current is 5.4 m/s [E]. She crosses the river in 425 seconds. Determine the width of the river

Omar swims across a river at a velocity of 2.50 m/s [30 o N of E] with respect to the water. The current is 5.4 m/s [E]. She crosses the river in 425 seconds. Determine the width of the river

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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Omar swims across a river at a velocity of 2.50 m/s [30 o N of E] with respect to the water. The current is 5.4 m/s [E]. She crosses the river in 425 seconds. Determine the width of the river.

Expert Solution
Step 1

Given:

Velocity of the Omar u = 2.5 m/s in [30 o N of E] 

velocity of the river v = 5.4 m/s in East direction

Time taken to cross the river is t = 425 seconds

Now according to the question Omar's effective velocity will be the resultant of the Omar's velocity with respect to the velocity of the river. as shown in the figure:

                                          Physics homework question answer, step 1, image 1

AB is the river width; 

Now from the figure the resultant velocity vector

v" =u2+v2+2uv cos(300)

v" =(2.5 m/s)2+(5.4 m/s)2+2(2.5 m/s)(5.4 m/s) cos(300)     =7.67 m/s

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