Based on the use of the modified Rayleigh criteria demonstrate mathematically which of these two surfaces will appear bright and dark in an Aircraft C-band radar image with a wavelength (λ) of 7.5 cm and an incident angle (θ) of 48 degree. The first surface is a uniform dry sand field with an average local height (h) of 0.10 cm. The second surface is a uniform cell of dry desert scrub vegetation averaging a local height (h) of 70 cm. Be sure to show the formulas you utilize, all your calculations, and explain your results.

Two point charges of charge Q = 19 nC and mass m = 27 g are 31 cm apart. One of them is let go. Gravity should be ignored. What will its speed be when it has moved 26 cm?

1: Can heat flow either into or out of a substance without the substance changing temperature? If not, why? If so, explain and give an example of such a process.

2: An ice cube can exist for many minutes while floating in water, even when the temperature of the water is greater than 0. Explain why.

If there are 3 quantum wells separated by the same distance in a 1-D array with wavefunction ψ1 ,
ψ2 , and ψ3 for these three quantum wells respectively. The electrons only acts on the
neighboring electrons with perturbation energy H’ = -|ΔE|. If the original eigen energy of ψ1 , ψ2 ,
or ψ3 is E1, try to use degenerate perturbation theory to calculate and sketch the new eigen
energies for this array with 3 quantum wells.

A particle of charge q and mass m is accelerated from rest through a potential difference V, after which it encounters a uniform magnetic field B perpendicular to its velocity v. If the particle moves in a plane perpendicular to B,

(a) Find an expression for the radius of its circular path in terms of q, V and B.

(b) If the particle is an electron, what must the potential difference be so it describes a circular path of radius 1.5 m in a magnetic field of 0.05 T?

(1) (A)You approach a stationary sound source with a speed such that the frequency of sound you hear is 17% greater than the actual frequency. With what speed are you approaching the sound source? Use the speed of sound in air as 343 m/s.

(B)Two trains approach each other on separate but adjacent tracks. Train 1 is traveling at a speed of 31.9 m/s and train 2 at a speed of 27.6 m/s. If the engineer of train 1 sounds his horn which has a frequency of 520 Hz, determine the frequency of the sound heard by the engineer of train 2. (Use 343 m/s as the speed of sound. Enter your answer to the nearest Hz.)

(C)Alice holds a small battery operated device used for tuning instruments that emits the frequency of middle C (262 Hz) while walking with a constant speed of 3.38 m/s toward a building which presents a hard smooth surface and hence reflects sound well. (Use 343 m/s as the speed of sound in air.) (A) Determine the beat frequency Alice observes between the device and its echo. (Enter your answer to at least 1 decimal place.) (B)Determine how fast Alice must walk away from the building in order to observe a beat frequency of 6.59 Hz.
m/s

The following questions about lasers:
a. Mention and explain the characteristics of the laser beam that distinguishes it from general light.
b. Write a summary of the working principles of the laser according to the assignment about the laser you have made.

A converging lens has a focal length of 7.5 cm.

(a) What are the image distances for objects placed at the following distances from the thin lens? Also, state if each image is real or virtual, upright or inverted, and enlarged or diminished in size.

(b) If the object is 5.00 cm high, what is the height of the image for the object distance of 5.0 cm and 25.0 cm?

Four charges are placed on the corners of a rectangle with length d = 0.00341 mm and breadth s = 0.00119 mm, as shown in the figure. The charges are given in terms of the elementary charge, e = +1.602×10‒19 C, as follows: q1 = q2 = +2000e and q3 = q4 = ‒3000e.

(a) Calculate the electric potential at point A, the middle of the rectangle, and at point B, the middle of the right-hand side of the rectangle.

(b) A particle with unknown charge q and mass m = 2.342 ×10‒20 kg is placed at point A, where it is initially at rest. The charge moves from point A to point B, where it has a speed of v = 12.23 m/s. Assuming that all forces apart from the electrostatic forces in the system are negligible, determine q. Use the answers obtained in (a) in your calculation.

(c) Would you be able to obtain the answer in (b) by using the equations of motion? Give a reason for your answer.

There are two identical, positively charged conducting spheres fixed in space. The spheres are 41.0 cm apart (center to center) and repel each other with an electrostatic force of F1 = 0.0600 N. Then, a thin conducting wire connects the spheres, redistributing the charge on each sphere. When the wire is removed the spheres still repel but with a force of F2 = 0.115 N. Using this information, find the initial charge on each sphere, q1 and q2 if initially q1<q2.

It takes 2.95 ms for the current in an LR circuit to increase from zero to 0.85 its maximum value.

Part A

Determine the time constant of the circuit.

Express your answer to two significant figures and include the appropriate units.

Part B

Determine the resistance of the circuit if L = 22.0 mH .

Express your answer to two significant figures and include the appropriate units.

1. Suppose you are driving a 500-kg Zamboni when it suddenly breaks down, forcing you to get out and push. You apply a force of 85 N on the machine, which experiences a constant frictional force of 5 N. How long (in seconds) will it take to push the Zamboni the remaining 40 m?

2. The coefficient of static friction between Kylo Ren's shoes and the floor of Starkiller Base is 0.21. How large (in Newtons) is the frictional force acting on his 90 kg body when he stands on an incline that forms an angle of 20^owith the horizontal?

3. A 4 kg box is placed on a ramp that forms an angle of 26^o with the horizontal. The coefficient of friction between the ramp and the box is 0.25. How long will it take the box to slide (from rest) 18 m to the bottom of the ramp?

4.

The Atwood machine is a simple device in which an object is suspended over a pulley and attached to another as shown:

Find the acceleration of block m₁ in m/s², assuming it has a mass of 9 kg and m₂ has a mass of 6 kg (ignore the mass of the pulley and friction in the axel).

5. While camping, you decide it is imperative to protect your beef jerky from those jerk raccoons that have been following you for miles. You suspend your cooler in the air, using two ropes tied to trees as shown:

Assuming =20^o and =35^o, find the tension in the rope on the left (in Newtons).

6. A tugboat traveling through Venice is pulling two smaller boats behind it using tow cables. The tugboat is connected to boat A, which has a mass of 300 kg and experiences a constant drag force of 70 N from the water. Boat A is connected via tow cable to boat B, which has a mass of 400 kg and experiences a drag force of 85 N. The tension in the cable between the tugboat and boat A is 2800 N. Find the acceleration of boat b (in m/s²).

7. A turtle is pushing a 2.5 kg rock across a flat surface through the desert. The turtle is applying a force of 10 N on the rock, which moves at a constant velocity. How much frictional force does the rock experience (in Newtons)?

8.

Consider the configuration shown below:

in which M₁ is being pulled up a ramp by M₂, which is descending due to the force of gravity. M₁ is experiencing a constant frictional force, which causes it to move at a constant velocity. If ,M₁ = 16 kg, and M₂ = 12 kg, what is the coefficient of friction between the block and the ramp? (ignore the mass of the pulley)

what is the short circuit current (Isc) and open circuit voltage (Voc) and how can I obtain those value from a I-V curve?

Define and discuss both ASTM grain size and Vickers hardness in details.
I need a full and detailed answer with references.