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°
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
