Needs clarity on this displacement vector diagram

Chijioke · Aug 31, 2023

Textbook page showing Example 1.2: a man crossing a 5 km wide river flowing east at 3 km/h, rowing at 10 km/h in still water, with parts (i) to (iv) asking for direction, resultant velocity, time, and drift.

The problem is actually a solved example

Two triangle diagrams: a velocity vector diagram with 3 km/hr across the top, 10 km/hr along the left side and angle θ; and a displacement vector diagram with a vertical 3 km arrow, an arrow pointing right, and X km along the top, with angle θ.

My attention is focused in understanding the displacement vector diagram as it has to deal with question (iv).
I have no problem understanding the velocity vector sketch below:

Vector diagram: point N on a horizontal line with an arrow pointing right, labelled 3 km hr-1, to point D; a line from N down to point E on a lower horizontal line, labelled 10 kmhr-1, with angle θ at E between the lines to N and D, captioned velocity vector.

As you can see ND is the velocity of the river current due East and NE is the velocity of the boat supposed the man chooses to go Northward.
Here comes another sketch for the velocity

Diagram of a displacement vector: point A at the bottom, a vertical arrow labelled 3 km to the north, a horizontal arrow labelled X km east to point H, with a dashed path from N to H and angle theta at A.

I am confused about the sketch because
a. I don't understand what the vertical arrow beside NA meant.
b. the 3km, is what? Is the displacement of the river or what? If it is, how was obtained because I know from the wording of the problem nothing like that was given. what was given 3 kmhr-1, which the displacement of the river. From the solving as it in the book I thinking that the 5km

Handwritten working: tan θ = 3/10 = x/5, with the x/5 part circled in blue ink; below, x = 15/10 = 1.5 km, with 1.5 km underlined.

As I showed here

Diagram of a displacement vector: point A at the bottom, a vertical line from A up to point N labelled 5 km, a horizontal line through N labelled X km to point M, and a line from A to M with angle θ at A.

Please help my understanding. Thank you.

kuruman · Aug 31, 2023

Chijioke said:

I am confused about the sketch because
a. I don't understand what the vertical arrow beside NA meant.
b. the 3km, is what? Is the displacement of the river or what? If it is, how was obtained because I know from the wording of the problem nothing like that was given. what was given 3 kmhr-1, which the displacement of the river. From the solving as it in the book I thinking that the 5km

You are understandably confused because the diagram provided in the solution is mislabeled. The vertical arrow beside NA must represent the vertical component of the displacement which is given as 5 km. The label 3 km is either a typo or the drawing is pasted from a different problem. Your drawing of the displacement vector is correct.

Chijioke · Aug 31, 2023

kuruman said:

You are understandably confused because the diagram provided in the solution is mislabeled. The vertical arrow beside NA must represent the vertical component of the displacement which is given as 5 km. The label 3 km is either a typo or the drawing is pasted from a different problem. Your drawing of the displacement vector is correct.

I may still have question concerning this but let go and think. Thank you.

Lnewqban · Aug 31, 2023

Chijioke said:

I am confused about the sketch because
a. I don't understand what the vertical arrow beside NA meant.

The river can't be made narrower: the man still has 5 km separating him from the opposite shore.
It must be a typo.

Needs clarity on this displacement vector diagram

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