The temperature in Winterberg is a sinusoidal function in time. 120 days ago, the temperature was at its maximum value of 55◦F. The tempearture has been falling since then, and 20 days from today it will reach its minimum value of 10◦F.

(a) Write a function f(t) in sinusoidal standard form for the temperature in Winterberg, in Fahrenheit, t days from today

b)People can only ski when the temperature is below 28◦F. Over the next 700 days (starting today), for how many days is it cold enough to ski? You can round all your answers to the nearest day.

A positive charge q is fixed at the point x=0,y=0 and a negative charge -2q is fixed at the point x=a,y=0.

Part A:

Derive an expression for the potential V at points on the y-axis as a function of the coordinate y. Take V to be zero at an infinite distance from the charges.

Part B:

At which positions on the y-axis is V = 0?

Part C:

What does the answer to part A become when y>>a?

Part D:

Explain why this result is obtained.

A parallel plate capacitor with plate separation d is connected to a battery. The capacitor is fully charged to Q Coulombs and a voltage of V. (C is the capacitance and U is the stored energy.) Answer the following questions regarding the capacitor charged by a battery. For each statement below, select True or False.

After being disconnected from the battery, inserting a dielectric with κ will increase U.
With the capacitor connected to the battery, decreasing d increases U.
With the capacitor connected to the battery, inserting a dielectric with κ will increase C.
With the capacitor connected to the battery, increasing d increases C.
After being disconnected from the battery, increasing d decreases V.
After being disconnected from the battery, inserting a dielectric with κ will decrease V.

We did an experiment : determination of entropy changes during melting of ice in a closed system. Can you write a 400 words paragraph introduction about The Second Law of Thermodynamics, entropy, entropy changes in reversible and irreversible processes, methods of calculating entropy changes in isothermal, isobaric and isochoric processes and entropy of the phase transformation.

In your own words. No copy-paste from the internet. Pleasee!!

In forensic science, it is useful to measure the speed at which firearms propel bullets. Before modern instruments, this was done with a device called a “ballistic pendulum”, consisting of a block of some soft material hanging from the end of a string. The experimenter fires a bullet into the block, which lodges into it; the block swings up at an angle. By measuring the angle, the experimenter can determine the velocity of the bullet.

Suppose that you are a detective trying to measure the velocity of the bullets fired from a particular gun. You construct a ballistic pendulum out of a string of length 50 cm and a clay block of mass 2 kg, and fire a bullet into it. If the bullet has a mass of 2.6 grams and the pendulum swings up to an angle 13.4 degrees, how fast was the bullet traveling when it struck the block?

Show all work and Thanks in advance!

Derive the energies for an infinite square well potential. Start from the Schrödinger Equation and show your work.

Please show all the work and steps and the math in details.
similar problem will be on my Exam, So I want to learn how to do this. Please write clear so I can read it.

Design a "bungee jump" apparatus for adults. A bungee jumper falls from a high platform with two elastic cords tied to the ankles. The jumper falls freely for a while, with the cords slack. Then the jumper falls an additional distance with the cords increasingly tense. Assume that you have cords that are 14 m long, and that the cords stretch in the jump an additional 20 m for a jumper whose mass is 80 kg, the heaviest adult you will allow to use your bungee jump (heavier customers would hit the ground). (a) It will help you a great deal in your analysis to make a series of 5 simple diagrams, like a comic strip, showing the platform, the jumper, and the two cords at the following times in the fall and the rebound: 1 while cords are slack (shown here as an example to get you started) 2 when the two cords are just starting to stretch 3 when the two cords are half stretched 4 when the two cords are fully stretched 5 when the two cords are again half stretched, on the way up On each diagram, draw and label vectors representing the forces acting on the jumper, and the jumper's velocity. Make the relative lengths of the vectors reflect their relative magnitudes. (b) At what instant is there the greatest tension in the cords? (How do you know?) When the person has fallen between 0 m and 14 m. When the person has fallen between 14 m and the bottom. At the top, when the person has fallen 0 m. At the bottom, when the person has fallen 34 m. When the person has fallen 14 m. (c) What is the jumper's speed at this instant, when the tension is greatest in the cords? v= m/s (d) Is the jumper's momentum changing at this instant or not? (That is, is dpy/dt nonzero or zero?) (e) Which of the following statements is a valid basis for answering part (d) correctly? A very short time ago the momentum was downward (and nonzero). Since the momentum is zero, the momentum isn't changing. If the momentum weren't changing, the momentum would remain zero forever. Since the net force must be zero when the momentum is zero, and since dpy/dt is equal to the net force, dpy/dt must be zero. After a very short time the momentum will be upward (and nonzero). the tolerance is +/-5% (f) Focus on this instant of greatest tension and, starting from a fundamental principle, determine the spring stiffness ks for each of the two cords. ks= N/m (g) What is the maximum tension that each one of the two cords must support without breaking? (This tells you what kind of cords you need to buy.) FT= N (h) What is the maximum acceleration |ay|=|dvy/dt| (in "g's") that the jumper experiences? (Note that |dpy/dt|=m|dvy/dt| | if v is small compared to c .) |ay|= g's (acceleration in m/s2 divided by 9.8 m/s2) (i) What is the direction of this maximum acceleration? (j) What approximations or simplifying assumptions did you have to make in your analysis which might not be adequately valid? (Don't check any approximations or simplifying assumptions which in fact have negligible effects on your numerical results.) Assume that the gravitational force hardly changes from the top of the jump to the bottom. Neglect air resistance, despite fairly high speeds. Assume the speeds are very small compared to the speed of light. Assume tension in cord proportional to stretch, even for the very large stretch occurring here.

1. The 6h 20 min between low and high tide is caused by what?
2. The 7 days between very large to mild CHANGES in tides is caused by what?
3. We see very large tide changes when the moon is in what two phases?              We see mild tide changes when the moon is in what two phases?
4. The unlit side of the moon ought to be totally black and be unseen in any phase. However, often it can be dimly seen. Why? How does it get any light at all?                    

5. Nebulas were mysterious fuzzy patches of light in space seen in a dark sky. Today we know these are four different things. List them.

6. Put these numbers in order, largest to smallest:   10⁵, 10¹⁴ , 10¹ , 10^-1 , 10^-8 ,10⁰

7. Put these distances in order: ly, megamile, pc, AU. How many km in 1 ly & 1 AU?

8. Put these 14 objects in rough size place (largest to smallest) according to their actual sizes, not as we see them: star (sun), major planet, comet head, meteor, galaxy, universe, a moon, asteroid, comet tail, solar system, local group, minor planet, space out to a nearby star, meteorite, an entire constellation

9. What is the moon illusion and why is it called an illusion?

The temperature right above the lake was 5°C, Your Grandpa said the lake wont crack, it is 65 feet deep and the temperature at the bottom of the lake is 20°C and he wanted to walk on the lake and start ice fishing. You didnt know if you should listen to Grandpa so you needed to calculate the thickness of the ice to see if it can hold. Your mass is 80 kg and your grandpas mass is 54 kg. Was Grandpa right?

A husband and wife take turns pulling their child in a wagon along a horizontal sidewalk. Each exerts a constant force and pulls the wagon through the same displacement. They do the same amount of work, but the husband's pulling force is directed 58° above the horizontal, and the wife's pulling force is directed 38° above the horizontal. The husband pulls with a force whose magnitude is 71 N. What is the magnitude of the pulling force exerted by his wife?

A block is projected up a frictionless inclined plane with initial speed v₀ = 3.48 m/s. The angle of incline is θ = 32.7°.

(a) How far up the plane does the block go?
___m

(b) How long does it take to get there?
___ s

(c) What is its speed when it gets back to the bottom?
___ m/s

Charge Q is uniformly distributed along a thin, flexible rod. The rod is then bent into a semicircle of radius R.

Find an expression for the electric potential at the center of the semicircle.

A proton with rest mass (.998GeV/c2) is moving with total energy E = 3GeV . What are its momentum

and its speed?