Posted by **Lisa** on Wednesday, March 23, 2011 at 11:51pm.

A boat in calm seas travels 19 km east and 32 km south. Find the distance and direction of the trip, relative to the south. What is the distance? What is the direction?

I'm confused about how to solve this problem. Could someone show me the steps?

- Math -
**Jai**, Thursday, March 24, 2011 at 1:12am
to get the resultant or the total distance, we use distance formula:

d = sqrt[ (x2-x1)^2 + (y2-y1)^2 ]

where

(x1,y1) is our reference/starting point, and

(x2,y2) is the final point

assuming our reference point is at the origin which is at (0,0)

d = sqrt[ (x2)^2 + (y2)^2 ]

substituting:

d = sqrt[ (19)^2 + (-32)^2 ]

d = 37.22 km

*note: we use -32 since it is travelling south/downward direction

getting the direction: let theta = angle from x-axis measured counterclockwise,,

tan (theta) = y/x

tan (theta) = (-32)/19

theta = -59.3 degrees

*note: the negative sign means opposite direction, or it is rotated clockwise

since we need the angle to be relative to south/y-axis,

90 - 59.3 = 30.7 degrees from south

thus distance = 37.22 km , 30.7 degrees from south

hope this helps~ :)

- Math -
**Lisa**, Thursday, March 24, 2011 at 2:36am
Thank you so much! This definitely helped! =)

## Answer This Question

## Related Questions

- Math - A boat in calm seas travels 19 km east and 32 km south. Find the distance...
- math - A boat in calm seas travels 13km east and 35 km north. Find the distance ...
- Physics - A current of a river flows steadily from west to east at 1.00 m/s. A ...
- Physics - Canadian geese migrate essentially along a north-south direction for ...
- Physics - A man walks the distance of 8km in a direction of 20degrees east the ...
- Physics - A jogger travels a route that has two parts. The first is a ...
- physics - A duck has a mass of 2.10 kg. As the duck paddles, a force of 0.110 N ...
- physics - A duck has a mass of 2.70 kg. As the duck paddles, a force of 0.130 N ...
- Math - Hi, I don't remember how to solve this. Please help me remember. "I live...
- Physics - A duck has a mass of 2.3 kg. As the duck paddles, a force of 0.08 N ...

More Related Questions