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?


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 displacement is 6.71 [m} and the angle is 63.4° to the north of east

Explanation:

Using a sketch showing Dante's displacement, we can find each of the points Dante moves through. First, it moves 4 blocks east, the new coordinate (4.0), then moves 3 blocks south and we will get the new coordinate (4, -3). Then Dante moves 1 block west, thus the new point is (3, -3). And finally it moves 9 blocks north where the new coordinate in and gets -3 - (-9) = + 6.

The displacement can be found using the equation for the straight line.

$d= \sqrt{(x_{1}-x_{0} )^{2} +(y_{1}-y_{0} )^{2} } \\d= \sqrt{(3-0 )^{2} +(6-0 )^{2} } \\\\d=6.71 [m]$

We can realize that the triangle formed is a right triangle, therefore we can find the angle of the displacement.

$tan(a)=\frac{6}{3} \\a=tan^-1(2)\\a=63.4[deg]$