Is the Distance Between Two Moving Boats Changing Over Time?

[pyrojelli]

1. Two boats start out 800 miles apart with boat A directly to the west of boat B. At the same time both boats start moving with boat A traveling to the east at 40mph while boat B travels north at 20mph. Determine if the distance between the boats is increasing, decreasing, or not changing after the following travel times: (a) 7 hours (b) 16 hours (c) 25 hours



2. I attempted to break apart their distances traveled by using component vector analysis. The distance between the two boats is the hypotenuse of whatever triangle they produce on the graph at a certain time. We want to find d'.



3. d'=? I park boat A at origin, therefore its cartesian coordinates are (0, 0), so boat B must be at (0, 800)

For part (a) I use vector components: A in x-direction: 400(7)=280 x-direction
So A is at (280, 0) since it does change in relation to y-axis (vice-versa for B)
B in y-direction: 20(7)=140 so B is (800, 140)
Base distance is 800-280=520 Height is just 140
I got the distance between them by using the distance formula: d=square root(520^2 + 140^2)= 538.516miles

How do I proceed to find h' ?

 

[pyrojelli]

From what I know, we can not use properties of similar triangles since the boats are moving at different rates.