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Calculate the resultant of two velocities of 6m/s and 8m/s acting at point 0 and angle of 45° with each other?
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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.
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Calculate the resultant of two velocities of 6m/s and 8m/s acting at point 0 and angle of 45° with each other?
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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?.
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