1.
Which of these expresses a vector quantity?
Correct Answer
D. 10 m/s to the east
Explanation
The answer "10 m/s to the east" expresses a vector quantity because it includes both magnitude (10 m/s) and direction (to the east). A vector quantity represents a physical quantity that has both magnitude and direction, such as velocity or force. In this case, the answer specifies a speed of 10 m/s and the direction of motion, which makes it a vector quantity.
2.
Which one of the following is an example of a vector quantity?
Correct Answer
C. Velocity
Explanation
Velocity is an example of a vector quantity because it has both magnitude and direction. It describes how fast an object is moving and in which direction it is moving. In contrast, area, mass, and distance are all examples of scalar quantities because they only have magnitude and do not have a specific direction associated with them.
3.
The order in which vectors are added will affect the end result.
Correct Answer
B. False
Explanation
The order in which vectors are added does not affect the end result. Vector addition is commutative, meaning that the result will be the same regardless of the order in which the vectors are added. This property holds true for both scalar and vector quantities. Therefore, the given statement is false.
4.
Vector A is directed northward and vector B is directed eastward. Which of the following vector addition diagrams best represent the addition of vectors A and B and the subsequent resultant?
Correct Answer
E. E
Explanation
In vector addition, the resultant vector is the vector sum of the individual vectors. In this case, since vector A is directed northward and vector B is directed eastward, the resultant vector should be directed in the northeast direction. Among the given options, only diagram E represents the addition of vectors A and B in a northeast direction, making it the best representation of the resultant vector.
5.
The vector sum (magnitude only) of 67.0 m, north + 38.0 m, south is 7382 m.
Correct Answer
B. False
Explanation
The vector sum of two quantities in opposite directions should result in a smaller magnitude, not a larger one. In this case, the magnitudes of 67.0 m and 38.0 m should add up to a value smaller than 67.0 m, not 7382 m. Therefore, the statement is false.
6.
Vectors in physics are equal to the amount of pressure.
Correct Answer
B. False
Explanation
The statement is incorrect. In physics, a vector is not the amount of pressure. A vector is a quantity that has both magnitude and direction. It represents physical quantities that require both magnitude and direction to be fully described, such as velocity, force, and displacement. Pressure, on the other hand, is a scalar quantity that only has magnitude and does not have a specific direction. Therefore, the correct answer is false.
7.
A vector is an object with a magnitude and a direction.
Correct Answer
A. True
Explanation
A vector is a mathematical object that represents both magnitude and direction. It is used to describe quantities such as velocity, force, and displacement. Unlike scalar quantities that only have magnitude, vectors have both magnitude and direction. Therefore, the statement that a vector is an object with a magnitude and a direction is true.
8.
When adding vector B to vector A geometrically (or graphically) using the head to the tail method, the resultant is drawn from ____ to the ____.
Correct Answer
C. The tail of A, head of B
Explanation
When adding vector B to vector A using the head-to-tail method, the resultant vector is drawn from the tail of A to the head of B. This method combines the magnitudes and directions of the vectors accurately. It's a fundamental technique in vector addition, commonly used in physics and engineering to determine the net effect of multiple forces or displacements acting on an object.
9.
Consider the magnitude and direction of vectors A and B as shown in Diagram 1 above. Which one of the following diagrams would represent B - A = R?
Correct Answer
B. Diagram B
Explanation
Diagram B represents B - A = R. In this diagram, vector A is represented by an arrow pointing to the left, and vector B is represented by an arrow pointing downwards. When we subtract vector A from vector B, we reverse the direction of vector A and add it to vector B. This results in a new vector R that points downwards and to the right, which is accurately represented in diagram B.
10.
The vector sum (magnitude only) of 25.0 m, north + 18.0 m, East is ___ m.
Correct Answer
C. 30.8
Explanation
The vector sum of 25.0 m, north and 18.0 m, east can be found using the Pythagorean theorem. The north and east components form the legs of a right triangle, with the vector sum as the hypotenuse. Using the Pythagorean theorem, the magnitude of the vector sum is calculated as the square root of the sum of the squares of the north and east components. In this case, the magnitude of the vector sum is √(25.0^2 + 18.0^2) = √(625 + 324) = √949 = 30.8 m. Therefore, the correct answer is 30.8.