A boat is traveling upstream at $11~\text{km/h}$ with respect to the water of a river. The water is flowing at $7.0~\text{km/h}$ with respect to the ground. What are the

(a) magnitude

(b) direction of the boat’s velocity with respect to the ground?

A child on the boat walks from front to rear at $6.0~\text{km/h}$ with respect to the boat.What are the

(c) magnitude

(d) direction of the child’s velocity with respect to the ground?

I wrote two vector equation for the two different situations:

$$V_{cg} = V_{cb}+V_{bg} \text{&} V_{bg} = V_{br}+V_{ra}$$

Using them I was able to come with the following

a) 4. b) upstream. c) -2 (incorrect) d) downstream.

My main issue as I have noted is with number c. It does not make sense to me why wouldn't it be $-2$. The operations is very simple and it is obvious that the direction of the child $6~\text{km}$ has to be negative because he is going downstream. All my other answers are correct; it is just this one that seems to be particularly troublesome as I cannot understand why due to the lack of operations involved.

  • $\begingroup$ I would take the -2 m/s to indicate that the child is actually moving upstream at 2 m/s. In essence, he is moving backwards. $\endgroup$
    – LDC3
    Jan 6, 2015 at 2:37
  • $\begingroup$ yes indeed that is why I originally submitted -2 as my answer but the system replied that it was wrong. $\endgroup$ Jan 6, 2015 at 2:46
  • $\begingroup$ The boat is moving 4 km/h upstream, the child walks at 6 km/h, the child is moving 2 km/h downstream, until he falls in the water, then he will be moving at 7 km/h. Ooops, I put m/s in the first comment instead of km/h. $\endgroup$
    – LDC3
    Jan 6, 2015 at 3:27

1 Answer 1


Magnitude is always positive. The direction is what determines the sign based on your axes. If upstream is defined as positive, then -2 is the vector's correct coordinate; but that's not what the question asks for.


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