Question

Help Please 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 displacement is 6.71[m] and the direction is 63.4° north east

Explanation:

Using as a tool the attached image where we can find a sketch of each of the movements done by Dante.

The initial point has coordinates (0,0) and then Dant moves 4 blocks to the east the new coordinate will be (4,0), after that he moves 3 blocks to the south the new coordinate will be (4,-3), the next displacement is one block to the west, in that case, the new point is (3,-3) and the final movement is 9 blocks to the north it means he moves from -3 - (-9) this operation will give us the final point in the y coordinate = +6.

Final Point = (3,6)

And using the equation for the distance of a straight line we have:

$d = \sqrt{(x_{1}-x_{0}  )^{2} +(y_{1} -y_{0} )^{2} } \\d= \sqrt{(3-0  )^{2} +(6-0 )^{2} }\\d= 6.7$

As we can realize we have a right triangle, so we can find easily the angle.

y = 6

x= 3

$tan(a)=\frac{y}{x} \\tan(a)=\frac{6}{3} \\\\a = tan ^-1(2 )\\a=63.43 (deg)$