Question

A boat sails for 2 hours at 35 mph in a direction 91.40°. How far south has it sailed (to the nearest mile)?

Answer 1

If it's traveling at 91.4 degrees, isn't that in the northwest direction? Or am I using the wrong starting point?

Answer 2

im not sure. thats how it is in the book

Answer 3

90 degrees is north unless you go -90 degrees then its south

Answer 4

Exactly...so you're looking for a negative value here? :P

Answer 5

oh ok

Answer 6

I'm not quite sure; that just seems like where it's going. xD
So, you're going to easily get a value for the magnitude of the direction, but you still have an angle. You want the portion of the motion that's in the north - south direction, so you can multiply that distance by cos(91.4-90) -- because you're only looking at that extra 1.4 degrees from north.

Answer 7

okay

Answer 8

so what would i multiply

Answer 9

You know how far the boat travels (d = v*t) and because you want the portion of the motion that's in line with north, you multiply by the cosine of that extra little bit of the angle. That's because cos(x) = adjacent/hypotenuse. The distance is your hypotenuse, so to get the adjacent side you get multiply the cosine by the distance.

Answer 10

okay thank you