Question

Dante is leading a parade across the main street in front of city hall. Starting at city hall, he marches the parade 4 blocks east, then 3 blocks south. From there, the parade marches 1 block west and 9 blocks north and finally stops. What is the vector displacement and direction of the the parade, starting from the city hall and the stopping point? (1 point)
Displacement: 6.71 m, Direction: 63.4 degrees north of east

Displacement: 8.01 m, Direction: 21.9 degrees north of east

Displacement: 2.56 m, Direction: 39.7 degrees north of east

Displacement: 4.31 m, Direction: 88.1 degrees north of east

Answer 1

Answer:

The correct option is A)

Displacement: 6.71 m, Direction: 63.4 degrees north of east

Explanation:

Given that Dante is leading a parade across the main street in front of city hall.

Let, Initial location of parade is 0i+0j

One block of city is one units on the XY- graph

Statement 1: Parade marches the parade 4 blocks east, then 3 blocks south

New location of parade is 4i-3j

Statement 2: The parade marches 1 block west and 9 blocks north and finally stops.

Final location of parade is (4i-3j)+(-1i+9j)=3i+6j

Displacement is given by

Displacement = (Final destination)-(Initial destination)

Displacement = (3i+6j)-(0i+0j)=3i+6j

Thus,

Magnitude of displacement = $\sqrt{3^{2}+6^{2}}$

                                              = 6.71 m

Direction of displacement =  $tan^{-1}(\frac{Y}{X} )$

                                           =  $tan^{-1}(\frac{6}{3} )$

                                           = 63.43 NE

Therefore, the correct option is A) Displacement: 6.71 m, Direction: 63.4 degrees north of east