Question

use the information and diagrams to answer the following question. student 1 walks as shown in diagram a, while student 2 walks as shown in diagram b. which statement correctly compares the magnitudes of the students displacements? a students 1 and 2 have an equal magnitude of displacement because the vector addition results in the same value. b student 1 has a greater magnitude of displacement because he walked a greater distance in the horizontal direction. c students 1 and 2 have an equal magnitude of displacements because the scalar addition results in the same value. d student 2 has a greater magnitude of displacement because she walked a greater distance in the vertical direction.

Explanation:

Step1: Recall displacement formula

Displacement is a vector. For two - dimensional displacements \(d_1\) and \(d_2\) in perpendicular directions, the magnitude of the net displacement \(D=\sqrt{d_1^{2}+d_2^{2}}\).

Step2: Calculate displacement for Student 1

For Student 1 in Diagram A, if the vertical displacement \(d_{1y} = 3m\) and the horizontal displacement \(d_{1x}=2m\), then the magnitude of the displacement \(D_1=\sqrt{3^{2}+2^{2}}=\sqrt{9 + 4}=\sqrt{13}m\).

Step3: Calculate displacement for Student 2

For Student 2 in Diagram B, with vertical displacement \(d_{2y}=2m\) and horizontal displacement \(d_{2x}=3m\), the magnitude of the displacement \(D_2=\sqrt{2^{2}+3^{2}}=\sqrt{4 + 9}=\sqrt{13}m\).

Step4: Compare displacements

Since \(D_1 = D_2=\sqrt{13}m\), students 1 and 2 have an equal magnitude of displacements because the vector addition results in the same value.

Answer:

A. Students 1 and 2 have an equal magnitude of displacements because the vector addition results in the same value.