# Homework Help: Basic constant velocity graph question

Tags:
1. Aug 14, 2015

### hahame

1. The problem statement, all variables and given/known data

A boat is sailing starting from x = 200m.
When interpreting x(position) vs. t(time) graph for this boat with math models x = -20t + 200(t<=10),
Is it right to say "The boat is approaching to the origin" ? (When t <= 10)

2. Relevant equations

x = -20t + 200(t<=10)

3. The attempt at a solution
I thought it would be yes, but wasn't sure why. What if the boat is moving diagonally? not directly to the origin?

Last edited: Aug 14, 2015
2. Aug 14, 2015

### SteamKing

Staff Emeritus
Boat? What boat?

Please provide a complete problem statement.

3. Aug 15, 2015

### stockzahn

That doesn't answer the original question, but here are some thoughts regarding the diagonal way:

In nautical terms there exists a word for the approaching speed to a goal, if it is not possible -due to which reasons ever – to sail directly in the preferred direction. It’s called VMG (velocity made good) and can be calculated with the actual boat speed over ground SOG multiplied with the cosine of angle α between the course over ground COG and the direction to the goal.

VMG = SOG ⋅ cos(α)

The larger α, the smaller the VMG and therefore the “approaching velocity” to the goal. Making way, the angle α increases and the VMG decreases (except if you point straight ahead to the goal, i.e. α = 0). The boat stops approaching to the goal, if the α = 90°. The distance Dlim, when this limit is reached can be calculated with the initial angle α0 at t=0.

Dlim = -200 ⋅ cos (α0)

The time tlim till this point is reached (assuming the SOG = -20) can be calculated:

tlim = Dlim / SOG

To answer your question in 3.: If -20 is the SOG and not the (partial) velocity in x-direction (i.e. there is the possibilty, that the boat moves “diagonally”), the boat will approach to the origin only till the time tlim, afterwards it will move away (and approaching doesn’t apply for all t<=10).

#### Attached Files:

• ###### PF_VMG.JPG
File size:
22.8 KB
Views:
111
4. Aug 15, 2015

### SteamKing

Staff Emeritus
That may be true, but the rules here at PF ask those seeking help to post complete problem statements, rather than snippets of a larger problem statement.

It gives prospective helpers all the facts and prevents needless speculation and going back and forth with the OP, trying to extract enough information to make sense of things.

5. Aug 15, 2015

### HallsofIvy

First, "approaching to the origin" is bad grammar! It should be just "approaching the origin". And "approaching the origin" just means that the distance to the origin decreases as time passes- it doesn't have to be along a straight line and it doesn't have to be directly toward the origin.