Here we see top views of three motorboats crossing a river....

Name: Problem 46, Chapter 3: Conceptual Physics
Uploaded: 2021-08-26T00:08:08-08:00
Duration: 12 min 47 s
Channel: Aparna Shakti
Description: Here we see top views of three motorboats crossing a river. All have the same speed relative to the water, and all experience the same river flow. Construct resultant vectors showing the speed and direction of each boat. Rank the boats from most to least for a. the time to reach the opposite shore. b. the fastest ride.

Here we see top views of three motorboats crossing a river. All have the same speed relative to the water, and all experience the same river flow. Construct resultant vectors showing the speed and direction of each boat. Rank the boats from most to least for a. the time to reach the opposite shore. b. the fastest ride.

Here we see top views of three motorboats crossing a river. All have the same speed relative to the water, and all experience the same river flow. Construct resultant vectors showing the speed and direction of each boat. Rank the boats from most to least for
a. the time to reach the opposite shore.
b. the fastest ride.

Key Concepts

Effective Speed

Effective speed refers to the magnitude of the resultant velocity vector, which determines how quickly an object moves relative to a fixed frame of reference. In river crossing problems, it affects both the overall ride duration and the time taken to reach the opposite shore.

Components of Motion

Decomposing vectors into components allows for the separation of movement in different directions, typically perpendicular and parallel to the river banks. This is crucial for analyzing how the boat’s efforts contribute to moving across the river versus being swept downstream.

Time Calculation in River Crossing

The time to cross a river is primarily determined by the component of the boat’s velocity that is directed perpendicular to the riverbank. Understanding this relationship is vital to ranking the boats according to how long they take to reach the opposite shore.

Relative Velocity

Relative velocity is the concept of determining the velocity of an object with respect to a particular frame of reference. In this context, it involves understanding the boat's speed relative to the water and how this combines with the river's flow to create the actual path taken relative to the shore.

Vector Addition

Vector addition is the method of combining two or more vectors to determine a resultant vector, taking into account both magnitude and direction. Here, it is used to combine the boat's velocity vector with the river's current vector to obtain the actual velocity and direction relative to the river bank.

Transcript

00:01 In this problem, it is given that here we see top views of the three motor boats crossing a river.

00:10 All have the same speed relative to the water, right? and all experience the same river flow.

00:20 Construct the resultant vectors showing the speed and direction of each boat.

00:28 Rank the boats from most to least per boat.

00:32 The time first the time to reach the opposite shirt and be the fastest right all right so here here we have these three boats given right so suppose this is a river right this is a river we have right this is a river so this is some kind of this river we can suppose here right so this is this is u .s.

01:11 Now we can say this is offshore, right? opposite offshore.

01:18 Opposite offshore.

01:22 So we need to know that this is offshore, opposite offshore, right? right? so we can say that this vectors are representing what? these vectors are representing us the direction of the boat moving, right? so can we make a resultant vector? yes.

01:53 So we know that this should be like this.

01:55 This is this is shown like it has this angle is more than 90.

02:01 Right.

02:01 So it is it will make rectangular.

02:05 You can you can say panellogram type of structure here.

02:11 You can say structure or you can say the diagram.

02:14 So this will be the resultant vector.

02:16 Right.

02:16 So this is resultant vector.

02:18 Now for this, this will be in a rectangular form.

02:23 Remember this because this is perpendicular for us right.

02:28 And remember, this is okay, so it should be, oh i'm sorry, it should be like this.