Abird flies 1,750 m north, and then 325 m east. calculate and draw the birds resultant displacement

Firstly it is important to explain what movement is and the difference between displacement and trajectory:

Movement is the change of position of a body at a certain time.  

Now, during this movement, the trajectory is the path followed by the body (is a scalar magnitude) and the displacement is the distance in a straight line between the initial and final position (is a vector magnitude).

For example, in the case of the bird flight here (1st figure attached), in a Cartesian coordinate plane where the origin is the initial position of the bird, the green arrows represent the trajectory of the bird, while the red arrow represents the resultant vector of the displacement of the bird.

This resultant vector (325,1750) is the result of a vector sum of the vectors (0,1750) and (325,0)

How do we calculate the module of the displacement?  

Well, after drawing the displacement vector, we are able to see that a Right Triangle (with a 90 degree angle) is formed (see 2nd figure attached) with two known sides and the third unknown.

This unknown side value (we will call it ) is the module of the displacement vector we want to find.

According to the Pythagorean Theorem:

In every right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the respective lengths of the legs (the other two sides of the triangle).

As shown in equation (1):

   (1)

Squaring both sides of the equation we have:

Then:

Which is the module of the displacement vector of the bird flight.

Now, if we want to find the direction of this displacement vector we have to use the sine trigonometric function:

    (2)

Where is the Opposite leg to the angle , and is the hypotenuse.

    (3)

In addition, we know the angles and sum to , so if we want to find the direction of the vector from the North, we have to find the value of as follows:

If

Then:

    (4)

We already know the value of angle from equation (3). Let’s substitute it on (4):

Finally, the resultant displacement of the bird is 1779.9227 m with a direction of East of North.

elly's long hair:

a. if the salon only takes cash, then this isn't the problem. it doesn't matter how much she has in her checking account.   she can't get a haircut until she has the cash.

b. if she has overdraft protection, then there's no problem.   she can go ahead and write a check that her account can't cover, then sometime later, pay the bank some outrageous usury for loaning her a few bucks for a few days, but with beautiful hair.

c. if elly has some principles, and doesn't want to write a bad check, then now she has a problem.   her desire for the new hairstyle is in conflict with her honesty and integrity.

d.   if the bank will not process a check she writes, then even if she had a million $$ in her account, she couldn't use any of it.   the amount she has in her account is not the problem.   and if i may suggest, she might as well close her checking account, and put the money where it'll work for her.   it's not doing her a bit of good in a checking account, since she can't write any checks.

justin can't pay the full balance:

a. he can't even handle the credit limit he has now.   under no circumstances should he ask for a higher limit.

b.   he can ask for the grace period to be extended.   but that's no solution, the bank will almost certainly refuse anyway, and there are much better options.   he knew the rules of his credit card when he started using it.

c.   he definitely should pay the interest on the balance, plus as much of the balance as he can cover at the same time.

d.   he definitely should pay the minimum otherwise they could shut down his card.   he should also pay as much more as he possibly can.   he should also remember the awkward situation he's in, stop buying stuff on credit that he can't afford, and avoid adding any more debt.

i'd say that justin's best best option isn't on this list of choices.   what he has to do:   pay as much as he can at least the minimum payment plus as much more as he can and then avoid adding more debt.

graph question answered .. you think better when you are relaxed and happy