Understanding Vectors: Homework Help and Tips for Solving Vector Problems

[Mike_Winegar]

I have been having a really rough time on my 3 homework problems tonight...I don't really understand vectors, so any help would be appreciated!

Sorry about the no LaTeX, I don't know how to do the vector sign

Anyway...

1.Given the Vectors U=2i(hat)-3j(hat)= <2,-3> and
V=-i(hat)+4j(hat)= <-1,4>, find:
a. U+V
b. 2U-3V
c. $$|V-U|$$

2.Draw a sketch to find each of the following graphically. (P and Q are in the attachment)
a. P+Q
b. P-3Q
c. -4P+4Q

On this one, my friend told me just to basically draw a triangle for each one of the problems, and the added third line to complete the triangle would equal the resultant vector. Is this right?

3.An airplane pilor needs to fly to a point 1800 km due east in a time of 6.0 hours. If a steady wind is blowing at 60 km/h from due south towards due north, calculate the velocity of the plane relative to the air (specifying both magnitude and direction) needed to achieve the pilot's objective.

I don't really know how side-winds affect flying objects being propelled at those speeds, some explanation on that would be appreciated to help solve the problem.

Thanks for your time taken for the help!

 

[QuantumCrash]

For the first one, change it matrices form which makes it easier to calculate and you simply and them or subtract them like you would with normal matrices.

Second, yes that would work. Make sure you've got the direction arrows right though.

Third, try resolving it in terms of vertical and horizontal. Basicaly, draw a diagram, that always work.

 

[andrevdh]

$$U = 2 \hat{i} - 3\hat{j}$$

$$V = -1\hat{i} + 4\hat{j}$$

a) $$U + V = 1\hat{i} + 1\hat{j}$$

see attachment for b)

 

[Max Eilerson]

'I don't really know how side-winds affect flying objects being propelled at those speeds, some explanation on that would be appreciated to help solve the problem. '

If your objective is due East, in what direction do you travel to get to that destination if a sidewind is trying to push you Northwards? If you just travel due East you will end up North of your destination...

 

[andrevdh]

Lets say that the airplane is flying along vector $$\vec{v_a}$$ and the wind is blowing along the vector $$\vec{v_w}$$ and his objective is to fly along $$\vec{v_o}$$. Then

$$\vec{V_o} = \vec{V_a} + \vec{V_w}$$

and since we know the magnitude and direction of the objective and wind vectors we require

$$\vec{V_a} = \vec{V_o} - \vec{V_w}$$

 

[HallsofIvy]

By the way, when you are flying, you are being supported by the air and must move as the air moves. It is not as if "a sidewind is trying to push you" in the same since that a strong wind might "try to push you" while you are walking on the sidewalk. It is like a toy car rolling across a table while the table is being carried to the side.

That's why the velocity of the wind is added to the velocity of the airplane.