A hotdog vendor named Sam is walking from the southwest corner of Central park to the Empire State Building. He starts at the intersection of 59th Street and Eighth Avenue, walks 3 blocks east to 59th Street and Fifth Avenue, and then 25 blocks south to the Empire State Building at the Corner of 34th Street and Fifth Avenue. Write his displacement vector in rectangular notation with units of "blocks." Orient the axes so positive y is to the north, and positive x is to the east. (b) A stockbroker named Andrea makes the same trip in a cab that gets lost, and detours 50 blocks south to Washington Square before reorienting and finally arriving at the Empire State Building. Is her displacement any different?

Question

A hotdog vendor named Sam is walking from the southwest corner of Central park to the Empire State Building. He starts at the intersection of 59th Street and Eighth Avenue, walks 3 blocks east to 59th Street and Fifth Avenue, and then 25 blocks south to the Empire State Building at the Corner of 34th Street and Fifth Avenue. Write his displacement vector in rectangular notation with units of "blocks." Orient the axes so positive y is to the north, and positive x is to the east. (b) A stockbroker named Andrea makes the same trip in a cab that gets lost, and detours 50 blocks south to Washington Square before reorienting and finally arriving at the Empire State Building. Is her displacement any different?

Answer 1

To find the displacement vector of Sam, we can use the formula:

Displacement = Final Position - Initial Position

For Sam:
Initial position: (59th Street and Eighth Avenue)
Final position: (34th Street and Fifth Avenue)

Now, we need to convert the streets into blocks. One block is equivalent to one street. Since Sam walks east 3 blocks, we move 3 blocks to the right (positive x direction). Then, he walks south 25 blocks, which means we move 25 blocks downwards (negative y direction).

Therefore, Sam's displacement vector is (-3, -25) blocks.

For Andrea:
Andrea makes a detour to Washington Square, which is 50 blocks south of her initial position. After that, she reorients and arrives at her final destination, the Empire State Building.

Since both of them end up at the same final destination, the displacement of Andrea will be the same as the displacement of Sam. So, Andrea's displacement vector is also (-3, -25) blocks.