Question

Persons X, Y, and Z walk along a circular path of radius 50 m. Person X walks halfway around the path, Person Y walks 3/4 of the way around the path, and Person Z walks completely around the path. Which of the following correctly lists the walkers in order of the magnitudes of their displacement vectors from the least to the greatest?

A. AX B. BX < Z < Y
C. CY < X < Z
D. DY < Z < X
E. EZ < Y < X

Answer 1

Persons X, Y, and Z walk along a circular path. The displacement vectors can be determined by calculating the lengths of their paths on the circle. The correct ordering of the walkers from least to greatest displacement vector magnitudes is AX.

Step-by-step explanation:

The displacement vector is a vector that represents the straight-line distance and direction from the starting point to the ending point of a movement. To determine the magnitude of the displacement vectors for persons X, Y, and Z, we need to calculate the lengths of their paths.

Person X walks halfway around the circular path, so their displacement vector will be half the circumference of the circle, which is 2πr/2 = πr. Person Y walks 3/4 of the way around the path, so their displacement vector will be 3/4 of the circumference of the circle, which is 3/4 * 2πr = 3/2πr. Person Z walks completely around the path, so their displacement vector will be the full circumference of the circle, which is 2πr.

With this information, we can arrange the walkers in order of their displacement vector magnitudes from least to greatest: AX, AY, AZ. Therefore, the correct answer is option A: AX.

Answer 2

E)
`\text{X}>\text{Y}>\text{Z}`

Step-by-step explanation:

GIVEN: Persons X, Y, and Z walk along a circular path of radius
`50\text{m}`. Person X walks halfway around the path, Person Y walks
`(3)/(4)` of the way around the path, and Person Z walks completely around the path.

TO FIND: Which of the following correctly lists the walkers in order of the magnitudes of their displacement vectors from the least to the greatest.

SOLUTION:

Consider the figure attached.

Displacement of X from start position
`=\text{radius}+\text{radius}`

`=2\text{radius}=100\text{m}`

Displacement of Y from start position
`=\sqrt{\text{radius}}`

`=√(50)=5√(2)\text{m}`

Displacement of Z from start position
`=0\text{m}`

As,
`\text{X}>\text{Y}>\text{Z}` option E is correct.