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

Answer:

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 $\frac{3}{4}$ 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 $=\sqrt{\text{radius}}$

                                                              $=\sqrt{50}=5\sqrt{2}\text{m}$

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

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