SOLUTION: A pilot mistakenly flies North 40 degrees West for 100 miles. Realizing his mistake, he flies North 10 degrees East for 125 miles to his destination. What was his total displacemen
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Question 890587: A pilot mistakenly flies North 40 degrees West for 100 miles. Realizing his mistake, he flies North 10 degrees East for 125 miles to his destination. What was his total displacement for the trip, and the angle/direction he should have traveled initially?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
north 40 degrees west is equivalent to 40 degrees west of north.
north 10 degrees east is equivalent to 10 degrees east of north.
the first picture shows the calculations for the vertical and horizontal component of the first part of his journey.
the second picture shows the calculations for the vertical and horizontal component of the second part of his journey.
the third picture shows overall impoact of combining the vertical components of the first part and the second part of his journey, and combining the horizontal components of the first part and the second part of his journey.
the overall horizontal part would be 64 miles west plus 22 miles east which get him a net distance of approximately 43 miles west.
the overall vertical part would be 77 miles north plus 123 miles north which gets him a net distance of approximately 200 miles north.
the overall angle is calculated at approximately 12 degrees west of north or, as is sometimes described, approximately north 12 degrees west.
the fourth picture shows you an overall view of his journey in approximate scale, so you can visualize how he went and how he should have gone.
the coordinate points are approximate to the nearest integer.
he traveled a total of 225 miles when, if he had gone straight from the beginning,l he would have only traveled 204 miles to his destination.
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