Suppose a particle of known mass and velocity collides with a second particle of known mass that is at rest. You try to solve for the final velocities of both particles in the plane of collision. How many unknowns could you possibly have to solve this problem

You could get by with 2 unknowns.

One final velocity and the character of the collision if the other final velocity is known

Both final velocities if the character of the collision is known.

Explanation:

You already have two known masses and both initial velocities.

The unknowns are two final velocities. Related to the two initial and two final velocities is the character of the collision.

We can already bracket the answers with the given information. The lower energy result being a perfectly in-elastic collision where the final velocity v is common to both and would be equal to the velocity of the Center of Mass of the system

m₁u₁ + m₂(0) = (m₁ + m₂)v

v = m₁u₁ / (m₁ + m₂)

The other end of the bracket would be the upper energy result from a perfectly elastic collision.  An elastic collision will have the relative velocity of approach equal the relative velocity of departure.

For approach the relative velocity is |u - 0| = u

For departure the relative velocity would be |v₂ - v₁| which will also = u.

Having one final velocity known is sufficient to solve the entire problem in either case.

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.

no

sodium is solid at rt