Question

2 boats leave the same port at the same time.

1 traveled at a speed of 30 mph heading N 50 E
The other traveled at a speed of 26 mph heading S 70 E

How far apart are the two boats after 1 hour?

Answer 1

Answer: Hi!

First, if you think that a compass has degrees as units, then N50E would be

50 degrees from north in the direction of the east, so if you put our 0 in east and count counterclockwise this will be an angle of 40 degrees.

If you think north has te Y axis positive direction, and east as the X axis positive direction. then the first boat has an angle of 40° counterclockwise from the +x

so the velocity in y is Vy=30mph*sin(40°) and in x is Vx= 30mph*cos(40°)

then the total displacement will be 22.98m to east and 19.28 north

the second one goes to s 70 e, so using the same notation as before, you can write this has -20° degrees count counterclockwise.

so decomposing the velocity will give us

Vy = 26*sin(-20°) and the displacement in Y is -8.89m

Vx = 26*cos(-20°) and the displacement in X is 24.43m

so the distance between the boats in y will be 19.28m - (-8.99)m = 28.27m

and in x: 24.43m - 22.98m = 1.45m

and the total distance is
`D^(2) = 1.45^(2) + 28.27^(2)`

so D = 28.30 m