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A river is flowing at a speed of 3m/s due east. A boat, whose speed in still water is 6m/s is steered in the direction due north. Find the angle made by resultant velocity of swimmer w.r.t river flow ? A) 30 degrees B) 37 degrees c) 53 degrees d) 60 degrees Correct answer is c. Can someone explain?
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A river is flowing at a speed of 3m/s due east. A boat, whose speed in...
The problem requires finding the angle made by the resultant velocity of the swimmer with respect to the river flow. To solve this problem, we can break down the velocities and use vector addition.
Given:
- River flow velocity: 3 m/s due east
- Boat speed in still water: 6 m/s
- Boat direction: due north
Let's break down the velocities into their components:
1. River flow velocity:
Since the river flow is due east, its velocity can be broken down into horizontal and vertical components.
- Horizontal component: 3 m/s (east)
- Vertical component: 0 m/s (north)
2. Boat velocity:
Since the boat is heading due north, its velocity can be broken down into horizontal and vertical components.
- Horizontal component: 0 m/s (east)
- Vertical component: 6 m/s (north)
Now, we can find the resultant velocity by adding the horizontal and vertical components of the river flow and boat velocities:
- Horizontal component: 3 m/s + 0 m/s = 3 m/s (east)
- Vertical component: 0 m/s + 6 m/s = 6 m/s (north)
Using the Pythagorean theorem, we can find the magnitude of the resultant velocity:
Resultant velocity = √((3 m/s)^2 + (6 m/s)^2)
= √(9 m^2/s^2 + 36 m^2/s^2)
= √(45 m^2/s^2)
= 3√5 m/s
To find the angle made by the resultant velocity with respect to the river flow, we can use trigonometry. The angle can be determined using the vertical and horizontal components of the resultant velocity:
tan(angle) = vertical component / horizontal component
tan(angle) = 6 m/s / 3 m/s
angle = atan(2)
angle ≈ 63.43 degrees
However, this angle represents the angle made by the resultant velocity with the positive x-axis. To find the angle with respect to the river flow, we need to subtract 90 degrees:
angle = 90 degrees - 63.43 degrees
angle ≈ 26.57 degrees
Therefore, the angle made by the resultant velocity of the swimmer with respect to the river flow is approximately 26.57 degrees.
Given:
- River flow velocity: 3 m/s due east
- Boat speed in still water: 6 m/s
- Boat direction: due north
Let's break down the velocities into their components:
1. River flow velocity:
Since the river flow is due east, its velocity can be broken down into horizontal and vertical components.
- Horizontal component: 3 m/s (east)
- Vertical component: 0 m/s (north)
2. Boat velocity:
Since the boat is heading due north, its velocity can be broken down into horizontal and vertical components.
- Horizontal component: 0 m/s (east)
- Vertical component: 6 m/s (north)
Now, we can find the resultant velocity by adding the horizontal and vertical components of the river flow and boat velocities:
- Horizontal component: 3 m/s + 0 m/s = 3 m/s (east)
- Vertical component: 0 m/s + 6 m/s = 6 m/s (north)
Using the Pythagorean theorem, we can find the magnitude of the resultant velocity:
Resultant velocity = √((3 m/s)^2 + (6 m/s)^2)
= √(9 m^2/s^2 + 36 m^2/s^2)
= √(45 m^2/s^2)
= 3√5 m/s
To find the angle made by the resultant velocity with respect to the river flow, we can use trigonometry. The angle can be determined using the vertical and horizontal components of the resultant velocity:
tan(angle) = vertical component / horizontal component
tan(angle) = 6 m/s / 3 m/s
angle = atan(2)
angle ≈ 63.43 degrees
However, this angle represents the angle made by the resultant velocity with the positive x-axis. To find the angle with respect to the river flow, we need to subtract 90 degrees:
angle = 90 degrees - 63.43 degrees
angle ≈ 26.57 degrees
Therefore, the angle made by the resultant velocity of the swimmer with respect to the river flow is approximately 26.57 degrees.
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A river is flowing at a speed of 3m/s due east. A boat, whose speed in still water is 6m/s is steered in the direction due north. Find the angle made by resultant velocity of swimmer w.r.t river flow ? A) 30 degrees B) 37 degrees c) 53 degrees d) 60 degrees Correct answer is c. Can someone explain?
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A river is flowing at a speed of 3m/s due east. A boat, whose speed in still water is 6m/s is steered in the direction due north. Find the angle made by resultant velocity of swimmer w.r.t river flow ? A) 30 degrees B) 37 degrees c) 53 degrees d) 60 degrees Correct answer is c. Can someone explain? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A river is flowing at a speed of 3m/s due east. A boat, whose speed in still water is 6m/s is steered in the direction due north. Find the angle made by resultant velocity of swimmer w.r.t river flow ? A) 30 degrees B) 37 degrees c) 53 degrees d) 60 degrees Correct answer is c. Can someone explain? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A river is flowing at a speed of 3m/s due east. A boat, whose speed in still water is 6m/s is steered in the direction due north. Find the angle made by resultant velocity of swimmer w.r.t river flow ? A) 30 degrees B) 37 degrees c) 53 degrees d) 60 degrees Correct answer is c. Can someone explain?.
A river is flowing at a speed of 3m/s due east. A boat, whose speed in still water is 6m/s is steered in the direction due north. Find the angle made by resultant velocity of swimmer w.r.t river flow ? A) 30 degrees B) 37 degrees c) 53 degrees d) 60 degrees Correct answer is c. Can someone explain? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A river is flowing at a speed of 3m/s due east. A boat, whose speed in still water is 6m/s is steered in the direction due north. Find the angle made by resultant velocity of swimmer w.r.t river flow ? A) 30 degrees B) 37 degrees c) 53 degrees d) 60 degrees Correct answer is c. Can someone explain? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A river is flowing at a speed of 3m/s due east. A boat, whose speed in still water is 6m/s is steered in the direction due north. Find the angle made by resultant velocity of swimmer w.r.t river flow ? A) 30 degrees B) 37 degrees c) 53 degrees d) 60 degrees Correct answer is c. Can someone explain?.
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A river is flowing at a speed of 3m/s due east. A boat, whose speed in still water is 6m/s is steered in the direction due north. Find the angle made by resultant velocity of swimmer w.r.t river flow ? A) 30 degrees B) 37 degrees c) 53 degrees d) 60 degrees Correct answer is c. Can someone explain?, a detailed solution for A river is flowing at a speed of 3m/s due east. A boat, whose speed in still water is 6m/s is steered in the direction due north. Find the angle made by resultant velocity of swimmer w.r.t river flow ? A) 30 degrees B) 37 degrees c) 53 degrees d) 60 degrees Correct answer is c. Can someone explain? has been provided alongside types of A river is flowing at a speed of 3m/s due east. A boat, whose speed in still water is 6m/s is steered in the direction due north. Find the angle made by resultant velocity of swimmer w.r.t river flow ? A) 30 degrees B) 37 degrees c) 53 degrees d) 60 degrees Correct answer is c. Can someone explain? theory, EduRev gives you an
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