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

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:

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

y = 6

x= 3

see the picture for the vector

the magnitude of the vector by pythagorean theorem

r = √( (-10)^2 + (3)^2 ) = √109

magnitude = √109 units

the direction angle between vector and x-axis is

tan^(-1)(3/10) = 16.699

so the direction is approximately 16.7 degrees north of west

as we know our atmosphere or air have different levels. every level has other gasses, and every gas has another permeability. when the light comes from lower permeability to higher permeability, it changes its direction. so that means that when the light comes from the moon to the earth, it changes it's direction many more times. it basically means that the shape of the light part of the moon is changed on the earth.

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