Two ships leave a harbor at the same time, traveling on courses that have an angle of 120 ° between them.

Question

If the first ship travels at 22 miles per hour and the second ship travels at 40 miles per hour, how far apart are the two ships after 1.7 hours?

What is the distance?

Answer 1

Imagine the first ship is sailing along the y axis and the second ship's course is 120 degrees from the first.  This would also mean that the second ship's course is 30 degrees below the x axis.  Now in 1.7 hours the first ship traveled (1.7)(22) = 37.4miles in the y direction. The second ship traveled (1.7)(40) = 68 miles in the direction 30 degrees below the x axis.  Break up the second ship's travels into x and y components.  so sin(30)*68 = 34 miles in the y direction.  And cos(30)*68 = 58.9 miles in the x direction.  Now add up the y components of ships 1 and 2 and we get 34 + 37.4 = 71.4 miles in the y direction.  then add up the x components 58.8 + 0 = 58.8 miles in the x direction.  Then we use the distance formula in 2 dimensions.

D = SQRT(x^2+y^2)

D = SQRT(58.8^2+71.4^2) = 92.5 miles

The ships are 92.5 miles apart.