Magnitude and Direction Word Problem

[slu1986]

1. The pilot of a small plane finds that the airport where he intended to land is fogged in. He flies 45 miles west to another airport to find that conditions there are too icy for him to land. He flies 20 miles at 15° east of south and is finally able to land at the third airport.

(a) How far and in what direction must he fly the next day to go directly to his original destination?

(b) How many extra miles beyond his original flight plan has he flown?


3. I know that you have to solve get the x and y components and plug them into the pythagorean theorem to get the resultant. And then do the arc tangent y/x to get the direction in degrees. I am just confused at how to set everything up. I figure that the x component of the 1st position is -45 mi since he is going west. and y - component is the sin (15) 20 mi = 5.17 mi. and plug these numbers into the pythagorean theorum = sqrt of -45^2 + 5.17^2 = 45.3 mi <---but i know this isn't right..So can someone please help me out and explain what I'm doing wrong and what I must do to do it correctly

 

[kuruman]

For the second leg, 20 miles at 15^o East of South the vector has both x and y components. What are they? Drawing a diagram of the whole trip should help.

 

[tms]

Take another look at the first leg, especially the $$y$$-component. As I read the problem, the first leg is due west.