The flagpole is held vertical by two ropes. The first of these ropes has a tension in it of 100 N and is at an angle of 60° to the flagpole. The other rope has a tension T, as shown. The resultant force is down the pole and of magnitude 200 N. In the space below, using a scale of 1 cm = 20 N, draw a scale drawing to find the value of the tension T. Clearly label 100 N, 200 N and T on your drawing

T₂ = 123.9 N,  θ = 66.2º

Explanation:

To solve this exercise we use the law of equilibrium, since the diaphragm does not appear, let's use the adjoint to see the forces in the system.

The tension T1 = 100 N, we create a reference frame centered on the pole

X axis

       T₁ₓ - = 0

        T_{2x}= T₁ₓ

Y axis y

      T_{1y} + T_{2y} - 200N = 0

      T_{2y} = 200 -T_{1y}

let's use trigonometry to find the component of the stresses

         sin 60 = T_{1y} / T₁

         cos 60 = t₁ₓ / T₁

         T_{1y} = T₁ sin 60

         T1x = T₁ cos 60

         T_{1y}y = 100 sin 60 = 86.6 N

         T₁ₓ = 100 cos 60 = 50 N

for voltage 2 it is done in the same way

         T_{2y} = T₂ sin θ

         T₂ₓ = T₂ cos θ

we substitute

           T₂ sin θ= 200 - 86.6 = 113.4

           T₂ cos θ = 50              (1)

to solve the system we divide the two equations

           tan θ = 113.4 / 50

           θ = tan⁻¹ 2,268

           θ = 66.2º

we caption in equation 1

           T₂ cos 66.2 = 50

           T₂ = 50 / cos 66.2

           T₂ = 123.9 N

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.

change tension