Question

Julianne went to a restaurant to have a taste of her favorite fried chicken and spaghetti. She drove 2 km, east and then 8.5 km, northeast. What is Julianne’s displacement from her origin?

Answer 1

Julianne’s displacement from her origin is equal to 10.015 kilometers.

Given the following data:

• Distance A = 2 km, East.

• Distance B = 8.5 km, Northeast.

To calculate Julianne’s displacement from her origin:

How to calculate displacement.

We would denote the two (2) unit vectors along the East and Northeast directions by i and j respectively.

Note: Northeast is at angle of 45° with the East.

In terms of vectors, the distances becomes:

Distance A = 2i

$Distance\;B=8.5 [(cos 45i + sin 45j)]\\\\Distance\;B=(\frac{8.5}{\sqrt{2} } i \;+\;\frac{8.5}{\sqrt{2} } j)$

For the resultant displacement:

$D^2 = [(2+\frac{8.5}{\sqrt{2} } )^2+ (\frac{8.5}{\sqrt{2} } )^2\\\\D =\sqrt{[(2+\frac{8.5}{\sqrt{2} } )^2+ (\frac{8.5}{\sqrt{2} } )^2} \\\\D=2+\frac{8.5}{\sqrt{2} } + \frac{8.5}{\sqrt{2} }$

D = 10.015 kilometers.

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