We can start by using vector addition to find the total displacement.
First, we need to convert the given directions into their corresponding components.
357 m [28.0o E of N] can be broken down into: - North component: 357 cos(28.0) = 311.6 m - East component: 357 sin(28.0) = 166.5 m
366 m [48.0o N of E] can be broken down into: - North component: 366 sin(48.0) = 266.5 m - East component: 366 cos(48.0) = 236.5 m
Now we can add the components to find the total displacement: - North component: 311.6 + 266.5 = 578.1 m - East component: 166.5 + 236.5 = 403.0 m
Using the Pythagorean theorem, we can find the magnitude of the total displacement: |d| = sqrt((578.1)^2 + (403.0)^2) = 700.6 m
To find the direction, we can use trigonometry: tan(theta) = (East component) / (North component) theta = atan((East component) / (North component))
Plugging in the values, we get: theta = atan(403.0 / 578.1) = 34.5o
Therefore, the direction of total displacement is 34.5o N of E.
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