Dante is leading a parade across the main street in front of city hall. Starting at city hall, he marches the parade 4 blocks ea
st, 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)
2 answers:
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°
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The magnitude of the net displacement is 95.3 m
Explanation:
To find the magnitude of the net displacement, we have to resolve each of the two displacements into the horizontal and vertical direction first.
1st displacement is:
at
So its components are
2nd displacement is:
at
So its components are
Therefore, the x- and y-components of the net displacement are:
Therefore, the magnitude of the final displacement is:
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