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)

Answer 1

Answer:

 R = 6.7  blocks and    θ = 63.4

Explanation:

The displacement vector is the vector sum of each individual displacement, the easiest way to do this is to find the magnitude of the displacement.

X axis

         x₁ = 4

         x₂ = -1

         x = 4 - 1 = 3

Y Axis  

      y₁ = -3

      y₂ = 9

      y = -3 + 9 = 6

We use the Pythagorean theorem

     R = √ (x² + y²)

     R =√ (3² + 6²)

     R = 6.7

We look for the displacement angle with trigonometry

        tan θ = y / x

       tan θ = 6/3

       θ = tan⁻¹ 2

       θ = 63.4

Answer 2

Answer:

The displacement between the city hall and the stopping point is 6.7 blocks.

The direction is 63.43°

Explanation:

The diagram explains better.

From the diagram, point O is the city hall and point D is the stopping point.

The displacement between O and D is OD.

Using Pythagoras theorem, we can find this:

OD² = OX² + DX²

From the diagram:

OX = 4 - 1 = 3 blocks

DX = 9 - 3 = 6 blocks

=> OD² = 3² + 6² = 9 + 36

OD² = 45

=> OD = 6.7 blocks

To get the direction, θ, we use SOHCAHTOA:

tanθ = DX/OX

tanθ = 6/3 = 2

=> θ = 63.43°