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$\bullet$ Crossing the river, I. A river flows due south with a speed of 2.0 $\mathrm{m} / \mathrm{s} .$ A man steers a motorboat across the river; his velocity relative to the water is 4.2 $\mathrm{m} / \mathrm{s}$ due east. The river is 800 $\mathrm{m}$ wide. (a) What is his velocity (magnitude and direction) relative to the earth? (b) How much time is required for the man to cross the river? (c) How far south of his starting point will he reach the opposite bank?

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Physics 101 Mechanics

Chapter 3

Motion in a Plane

Physics Basics

Motion Along a Straight Line

Motion in 2d or 3d

Newton's Laws of Motion

Cornell University

Simon Fraser University

University of Winnipeg

Lectures

03:28

Newton's Laws of Moti…

04:16

In mathematics, a proof is…

05:52

Crossing the River I. A ri…

03:39

03:50

A river flows due south wi…

01:07

A river is moving east at …

05:20

A 200 -m-wide river flows …

05:18

$\bullet$ Crossing the riv…

04:50

Crossing the River I. (a) …

05:28

A 200 -m-wide river has a …

07:03

(a) In which direction sho…

01:52

A motorboat heads due east…

01:39

Two speedboats are traveli…

02:20

A river flows due east at …

03:54

Velocity of a Boat A strai…

06:45

02:15

A kayaker needs to paddle …

01:42

A swimmer can swim in stil…

02:23

You are boating on a river…

04:49

A boat can be rowed at 8.0…

03:25

Velocity of a Boat $A$ str…

02:58

A boy is attempting to swi…

So let's draw was happening here. He has the triangle, and this factor going to the right will be the velocity of thie boat relative to the water. And then here we have the velocity of thie water relative to the earth. And then here we have the velocity of the boat relative to the earth. Ah, we have Seita here and right here. This will also equal Seita due to the alternate angle through, Um um rather alternate interior angle through, um and so we can say that the velocity brother, they're giving us that the velocity of the water relative to earth is going to be due south, so negative 2.0 meters per second. This is again just the magnet. This is the magnitude. And they were going to say that the velocity of the boat relative to the water is equal in 4.2 meters per second due east. So south peace. And then the question is asking us, What's the what's the magnitude of the velocity of the boat relative to the earth? So we can say that the velocity of the boat relative to the earth is going to be equal. Teo negative. Two squared plus 4.2 squared all to the 1/2 power and this is equaling 4.65 meters per second. And so this would be the magnitude of the boat magnitude of the velocity of the boat relative to the earth. And we can say that the direction will be arc tangent of the wide component so negative, too divided by 4.2. And this is equaling 25.5 degrees and me to specify direction. So 25.5 degrees below positive ex access or one can also say south of east. So that would be your answer. This this the magnitude and the direction would be your answer for apart, eh? And then Part B is asking us for the time so time would simply be equal to doubt. Tow acts divided by the act, the velocity in the ex direction. This would be simply 800 meters divided by the velocity of the boat relative to the water. So this would be 4.2 and this would equal 190 0.5 seconds, and then they're asking us the distance traveled during that time in the UAE direction. So the velocity of the water relative to the earth is going to be negative two meters per second. So this would simply be negative too. Times 190.5 seconds. And this would give us 381 meters again. This is negative. So where you have moved south and here, rather 100 meters would be assuming east This Oh, these equations on ly work because there is no acceleration in either of these directions either. Otherwise, you're going to have to use the Kinnah Matic. The three can a matic equations in order. Teo, tackle this problem. But again hear the acceleration, the acceleration here, zero for both directions. So you can just a substitute directly and again, you know T equals 195 190.5 seconds and delta y equals 381 meters south. That is the end of the solution. Thank you for watching

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