As astronaut visiting Planet X, you’re assigned to measure the free-fall acceleration. Getting out your meter stick and stopwatch, you time the fall of a heavy ball from several Heights. You data is as follows: Height (m) Fall Time (s)
0.0 0.00
1.0 0.54
2.0 0.72
3.0 0.91
4.0 1.01
5.0 1.17
a.) Analyze these data to determine the free-fall acceleration on Planet X. Your analysis should involve fitting a straight lie to an appropriate graph. Place the graph here. (Hint Kinematics)
b.) Determine the uncertainty in the free-fall acceleration.

g = (0.13 + - 0.05) m / s²

Explanation:

a) The equations of physics are valid in all inertial systems, therefore the kinematic relationships on this planet are the same as on Earth.

        y = v₀ t - ½ g t²

From the statement it follows that the body is released, so its initial velocity is zero

        y = 1/2 g t²

where we take the downward direction as positive

With this expression to make a linear graph we must graph t² vs y, see attached.  Observe that the controlled variable is the height, so this is the independent variable and must go on the x axis, the values of the slope and point of cut can be obtained from this graph  by lineal regretion

           y ’= m x + b

           y ’= 0.2668 x + 0.00406

If we compare this equation of the line with the equation of free fall

          y ’= t2

          x = y

          m = 0.2668

          b = 0.00406

Since the value of b is very small, we can say that our assumption that the initial velocity is zero is correct.

Now we can compare the expressions of free fall and the equation of the line obtained

             y = ½ g t2

             y ’= m x

to be functionally equivalent

            x = 1 / m y '

now we can see the slope

          1 / m = ½ g

          g = 2 / m

          g = 2 / 0.2668

          g = 7.496 m / s²

b) the uncertainty of the acceleration is

          Δg = dg/dm   Δm

the uncertainty of m is given by the fit of the linear regression of the program Δm = 0.025

          dg / dm = 1 / 2m

           Δg = 1 /2m  Δm

           Δg = 1 / (2 0.2668) 0.025

           Δg = 0.047

The result of this exercise with the correct significant figures

          g = (0.13 + - 0.05) m / s²

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.

come closer and become far apart and become steam/gas