Starting in Albany, you travel a distance 319 miles in a direction 22.3 degrees north of...

Starting in Albany, you travel a distance 319 miles in a direction 22.3 degrees north of west. Then, from this new position, you travel another distance 360 miles in a direction 11.0 degrees north of east. In your final position, what is your displacement from Albany?

		679 miles 33.3 degrees North of West
		844 miles 23.5 degrees North of West
		679 miles 33.3 degrees North of East
		198 miles 72.9 degrees North of West

Solutions

Expert Solution

Let us assign coordinate axes to the directions, with Albany at the origin.

North	Positive Y-axis
South	Negative Y-axis
East	Positive X-axis
West	Negative X-axis

For the first part, the travel is 319 miles at 22.3 degrees north-of-west.

Using the coordinate axes, we can see that

The X-component of displacement is

The Y-component of displacement is

For the second part, the travel is 360 miles at 11 degrees north-of-east.

The X-component of displacement is

The Y-component of displacement is

Therefore, the total distance traveled along the X-axis is

The total distance traveled along the Y-axis is

The displacement magnitude is then

The angle at which this displacement is

However, this angle is measured from the positive X-axis, i.e the East direction.

Therefore, the correct answer is

at North of East

genius_generous answered 1 month ago

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