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A vector A makes an angle of 20 degree and vector B makes an angle of 110 degree with the X axis. The magnitudes of these vectors are 3m and 4m respectively. Find the resultant.?
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A vector A makes an angle of 20 degree and vector B makes an angle of ...
Problem Statement
A vector A makes an angle of 20 degree and vector B makes an angle of 110 degree with the X axis. The magnitudes of these vectors are 3m and 4m respectively. Find the resultant. Explain in detail.
Solution
To solve this problem, we will use the vector addition formula:
C = A + B
where C is the resultant vector, A and B are the given vectors.
Step 1: Resolve the Vectors
Resolve the given vectors into their x and y components using the following formulas:
Ax = A cos θ
Ay = A sin θ
Bx = B cos θ
By = B sin θ
where θ is the angle the vector makes with the x-axis.
Using these formulas, we get:
Ax = 3 cos 20° = 2.828 m
Ay = 3 sin 20° = 0.998 m
Bx = 4 cos 110° = -1.305 m
By = 4 sin 110° = 3.648 m
Step 2: Add the Components
Add the x and y components of the vectors to get the x and y components of the resultant vector:
Cx = Ax + Bx
Cy = Ay + By
Substituting the values, we get:
Cx = 2.828 - 1.305 = 1.523 m
Cy = 0.998 + 3.648 = 4.646 m
Step 3: Find the Magnitude and Direction of the Resultant Vector
Using the components of the resultant vector, we can find its magnitude and direction:
C = √(Cx² + Cy²)
θ = tan⁻¹(Cy/Cx)
Substituting the values, we get:
C = √(1.523² + 4.646²) = 4.829 m
θ = tan⁻¹(4.646/1.523) = 72.69°
Step 4: Final Answer
Therefore, the magnitude of the resultant vector is 4.829 m and it makes an angle of 72.69° with the x-axis.
Community Answer
A vector A makes an angle of 20 degree and vector B makes an angle of ...
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A vector A makes an angle of 20 degree and vector B makes an angle of 110 degree with the X axis. The magnitudes of these vectors are 3m and 4m respectively. Find the resultant.?
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A vector A makes an angle of 20 degree and vector B makes an angle of 110 degree with the X axis. The magnitudes of these vectors are 3m and 4m respectively. Find the resultant.? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A vector A makes an angle of 20 degree and vector B makes an angle of 110 degree with the X axis. The magnitudes of these vectors are 3m and 4m respectively. Find the resultant.? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A vector A makes an angle of 20 degree and vector B makes an angle of 110 degree with the X axis. The magnitudes of these vectors are 3m and 4m respectively. Find the resultant.?.
A vector A makes an angle of 20 degree and vector B makes an angle of 110 degree with the X axis. The magnitudes of these vectors are 3m and 4m respectively. Find the resultant.? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A vector A makes an angle of 20 degree and vector B makes an angle of 110 degree with the X axis. The magnitudes of these vectors are 3m and 4m respectively. Find the resultant.? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A vector A makes an angle of 20 degree and vector B makes an angle of 110 degree with the X axis. The magnitudes of these vectors are 3m and 4m respectively. Find the resultant.?.
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