UPSC Exam > UPSC Questions > Calculate the resultant of two velocities of ...
Start Learning for Free
Calculate the resultant of two velocities of 6m/s and 8m/s acting at point 0 and angle of 45° with each other?
Most Upvoted Answer
Calculate the resultant of two velocities of 6m/s and 8m/s acting at p...
Understanding Resultant Velocity
When two velocities are acting at an angle, their resultant can be calculated using the law of cosines. In this case, we have two velocities:
- Velocity 1 (V1) = 6 m/s
- Velocity 2 (V2) = 8 m/s
- Angle (θ) = 45°
Resultant Velocity Formula
To find the magnitude of the resultant velocity (R), we use the formula:
R = √(V1² + V2² + 2 * V1 * V2 * cos(θ))
Step-by-Step Calculation
1. Square the Velocities:
- V1² = 6² = 36
- V2² = 8² = 64
2. Calculate Cosine of the Angle:
- cos(45°) = √2 / 2 ≈ 0.7071
3. Calculate the Cross Term:
- 2 * V1 * V2 * cos(θ) = 2 * 6 * 8 * 0.7071 ≈ 67.882
4. Sum the Values:
- R² = 36 + 64 + 67.882 = 167.882
5. Take the Square Root:
- R = √167.882 ≈ 12.94 m/s
Final Result
The resultant velocity of the two vectors acting at a 45° angle is approximately:
- R ≈ 12.94 m/s
Conclusion
The resultant velocity combines the effects of both velocities acting at an angle, resulting in a stronger net velocity of 12.94 m/s. This calculation is essential in physics for understanding motion in multiple dimensions.
When two velocities are acting at an angle, their resultant can be calculated using the law of cosines. In this case, we have two velocities:
- Velocity 1 (V1) = 6 m/s
- Velocity 2 (V2) = 8 m/s
- Angle (θ) = 45°
Resultant Velocity Formula
To find the magnitude of the resultant velocity (R), we use the formula:
R = √(V1² + V2² + 2 * V1 * V2 * cos(θ))
Step-by-Step Calculation
1. Square the Velocities:
- V1² = 6² = 36
- V2² = 8² = 64
2. Calculate Cosine of the Angle:
- cos(45°) = √2 / 2 ≈ 0.7071
3. Calculate the Cross Term:
- 2 * V1 * V2 * cos(θ) = 2 * 6 * 8 * 0.7071 ≈ 67.882
4. Sum the Values:
- R² = 36 + 64 + 67.882 = 167.882
5. Take the Square Root:
- R = √167.882 ≈ 12.94 m/s
Final Result
The resultant velocity of the two vectors acting at a 45° angle is approximately:
- R ≈ 12.94 m/s
Conclusion
The resultant velocity combines the effects of both velocities acting at an angle, resulting in a stronger net velocity of 12.94 m/s. This calculation is essential in physics for understanding motion in multiple dimensions.
Attention UPSC Students!
To make sure you are not studying endlessly, EduRev has designed UPSC study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in UPSC.
|
Explore Courses for UPSC exam
|
|
Top Courses for UPSCView all
Calculate the resultant of two velocities of 6m/s and 8m/s acting at point 0 and angle of 45° with each other?
Question Description
Calculate the resultant of two velocities of 6m/s and 8m/s acting at point 0 and angle of 45° with each other? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Calculate the resultant of two velocities of 6m/s and 8m/s acting at point 0 and angle of 45° with each other? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Calculate the resultant of two velocities of 6m/s and 8m/s acting at point 0 and angle of 45° with each other?.
Calculate the resultant of two velocities of 6m/s and 8m/s acting at point 0 and angle of 45° with each other? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Calculate the resultant of two velocities of 6m/s and 8m/s acting at point 0 and angle of 45° with each other? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Calculate the resultant of two velocities of 6m/s and 8m/s acting at point 0 and angle of 45° with each other?.
Solutions for Calculate the resultant of two velocities of 6m/s and 8m/s acting at point 0 and angle of 45° with each other? in English & in Hindi are available as part of our courses for UPSC.
Download more important topics, notes, lectures and mock test series for UPSC Exam by signing up for free.
Here you can find the meaning of Calculate the resultant of two velocities of 6m/s and 8m/s acting at point 0 and angle of 45° with each other? defined & explained in the simplest way possible. Besides giving the explanation of
Calculate the resultant of two velocities of 6m/s and 8m/s acting at point 0 and angle of 45° with each other?, a detailed solution for Calculate the resultant of two velocities of 6m/s and 8m/s acting at point 0 and angle of 45° with each other? has been provided alongside types of Calculate the resultant of two velocities of 6m/s and 8m/s acting at point 0 and angle of 45° with each other? theory, EduRev gives you an
ample number of questions to practice Calculate the resultant of two velocities of 6m/s and 8m/s acting at point 0 and angle of 45° with each other? tests, examples and also practice UPSC tests.
|
|
Explore Courses for UPSC exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup