Scalar And Vector Quantities - SS1 Physics Past Questions and Answers - page 4
In a right-angled triangle, the vertical component of a vector is given by:
The magnitude of the vector multiplied by the sine of the angle.
The magnitude of the vector multiplied by the cosine of the angle.
The magnitude of the vector divided by the sine of the angle.
The magnitude of the vector divided by the cosine of the angle.
In a right-angled triangle, the horizontal component of a vector is given by:
The magnitude of the vector multiplied by the sine of the angle.
The magnitude of the vector multiplied by the cosine of the angle.
The magnitude of the vector divided by the sine of the angle.
The magnitude of the vector divided by the cosine of the angle.
The sum of the components of a vector is equal to:
The magnitude of the vector.
The direction of the vector.
The vector itself.
The magnitude and direction of the vector.
When resolving a vector into components, the magnitude of the resultant vector is equal to:
The sum of the magnitudes of the components.
The difference of the magnitudes of the components.
The product of the magnitudes of the components.
The division of the magnitudes of the components.
When resolving a vector into components, the direction of the resultant vector is determined by:
The magnitudes of the components.
The difference of the magnitudes of the components.
The product of the magnitudes of the components.
The angle between the vector and the coordinate axes.
The resolution of a vector into its components is a useful technique in:
Vector addition.
Vector subtraction.
Vector multiplication.
Vector division.
The resolution of a vector into its components is most commonly used in which branch of physics?
Mechanics.
Thermodynamics.
Optics.
Electricity and magnetism.
The resolution of a vector into its components allows for the analysis of:
Motion in one dimension.
Motion in two dimensions.
Motion in three dimensions.
Motion in any number of dimensions.
A force vector F has a magnitude of 10 N and is directed at an angle of 60 degrees with the x-axis. Resolve the force vector into its x and y components.
Given:
Magnitude of force (F) = 10 N
Angle with x-axis (θ) = 60 degrees
To find the x and y components, we can use the following trigonometric relationships:
Fx = F X cos(θ)
Fy = F X sin(θ)
Calculating the components:
Fx = 10 N X cos(60 degrees) = 10 N X 0.5 = 5 N
Fy = 10 N X sin(60 degrees) = 10 N X 0.866 = 8.66 N
The x component of the force vector is 5 N, and the y component is 8.66 N.
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A displacement vector D has a magnitude of 12 m and is directed at an angle of 45 degrees with the positive x-axis. Resolve the displacement vector into its x and y components
Given:
Magnitude of displacement (D) = 12 m
Angle with the x-axis (θ) = 45 degrees
To find the x and y components, we can use the same trigonometric relationships:
Dx = D X cos(θ)
Dy = D X sin(θ)
Calculating the components:
Dx = 12 m X cos(45 degrees) = 12 m X 0.707 = 8.49 m
Dy = 12 m X sin(45 degrees) = 12 m X 0.707 = 8.49 m
The x component of the displacement vector is 8.49m, and the y component is 8.49m.
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