Final answer:
The Pythagorean theorem can be used to calculate the resultant vector of two perpendicular vectors, which is true. Displacement is the same for two people walking in a block regardless of their path, so the statement about different displacements is false. Superposition of waves can occur with different frequencies, making the statement about superposition true.The correct option is A.
Step-by-step explanation:
True or False: We can use the Pythagorean theorem to calculate the length of the resultant vector obtained from the addition of two vectors which are at right angles to each other. The answer is a. True. The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. When two vectors are at right angles, you can consider them as forming a right-angled triangle with the resultant vector as the hypotenuse. Therefore, you can use the Pythagorean theorem to find the magnitude of the resultant vector.
True or False: A person walks 2 blocks east and 5 blocks north. Another person walks 5 blocks north and then two blocks east. The displacement of the first person will be more than the displacement of the second person. The answer is b. False. Displacement is a vector quantity that refers to the overall change in position. In both scenarios, the starting and ending points are the same, regardless of the path taken. Therefore, the displacements are equal and the direction is the same for both persons.
True or False: Waves can superimpose if their frequencies are different. The answer is a. True. Superposition is the phenomenon where two or more waves pass through the same point in space, their displacements add together at every point. This is possible even if the waves have different frequencies.