I have two ambiguous questions that I could not understand from my worksheet other day in physics class.

 

I was wondering if my answers were right so please help me.

 

(I do not remember exact wording)

 

1. I'm traveling south with my boat 3 m/s relative to the river. The river's flowing east 2 m/s relative to the shore. Then my vector relative to the shore will

a) slightly decrease

b) slightly increase

c) no change

 

I put B because I thought that, "Hey, this sounds like Pythagorean Relationship" but I'm not sure.

 

2. When adding vectors, the length and direction of each vector must be

a) similar to the that of resultant vector

b) not changed

c) reversed

 

I put B because I thought that vectors can be shifted around AS LONG AS their displacement was same. A sounds like plausible answer though.

You're right that these questions are poorly worded, especially the first one. The problem doesn't say anything about changing speeds, however the resultant velocity will be larger than either of the components.

Number 2 is correct. You can move vectors around as long as you don't change the length or the direction. This is a very important property of vectors.

These are dreadfully worded. Whomever made these up needs firing. As Neonblack said, the answers they want are probably b both times, but it is difficult to know what they are trying to ask.

 

For question 1, you are right about Pythogoras' Theorem. Your speed relative to the shore will be [math]\sqrt{(3m/s)^2+(2m/s)^2} = \sqrt{9+4}m/s=\sqrt{13}m/s \approx 3.6m/s[/math] at an angle [math]\tan^{-1} (3/2)[/math] to the south of the direction of flow of the river.

Thank you!

 

Yeah, I need to get better physics teacher.. arggg