A diver springs off a 10 m high diving board. If he leaves the board with an initial upward velocity of 5.0 m/sec,
a.) How high will he rise above the diving board?
b.) How long will he be in the air before he hits the water?

Tom, Spock, and McCoy stand on the top deck of a parking garage on planet Earth, 17 m above the ground below. For reasons that are unknown to us, they simultaneously throw pebbles off the deck, each at the same speed of 8 m/s. Tom throws his up at an angle of 45 degrees above the horizontal, Spock throws his perfectly horizontally, and McCoy, in a fit of pique, throws his straight down toward the ground. How far does Tom's stone land from the edge of the garage in meters?

Ball A of mass 0.55 kg has a velocity of 0.65 m/s east. It strikes a stationary ball, also of mass 0.55 kg. Ball A deflects off ball B at an angle of 37° north of A's original path. Ball B moves in a line 90° right of the final path of A. Find the momentum (in kg m/s) of Ball A after the collision.

A nucleus has atomic mass of 144. In which of the following cases could the nucleus be stable?

A) The nucleus may be stable if it has between 73 and 83 protons.

B) The nucleus may be stable if it has between 144 and 288 protons.

C) The nucleus may be stable if it has between 83 and 144 protons

D) The nucleus may be stable if it has more than 288 protons

E) None of the the cases described here would allow the nucleus to be stable.

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You are hired by an automotive company to choose a spring to use on each of the four wheels of a 2000 kg racing vehicle designed to go 180 miles per hour. When you set the car on the tires the entire car is supposed to sag not more than 10 cm. The car also needs shocks to damp out road vibrations. The damping constant should be chosen such that the amplitude of oscillation reduces to 1/3 the original undamped amplitude after one full period of oscillation. Give values for k, the spring constant, and b, the damping constant. State any other assumptions you might need to make.

The electric component of a beam of polarized light is Ey = (5.10 V/m) sin[(1.16 × 106 m-1)z + ωt]. (a) Write an expression for the magnetic field component of the wave, including a value for ω. What are the (b) wavelength, (c) period, and (d) intensity of this light? (e) Parallel to which axis does the magnetic field oscillate? (f) In which region of the electromagnetic spectrum is this wave?

Two people are carrying a uniform 3 m long steel beam that has a total mass of 32.1 kg. One person is supporting it at the far left end with an upward force of 120 N, while the second one is supporting it somewhere near the right end with an unknown force.

How much force is required from the second person in order to balance the beam? H

ow far from the right end must the second person lift in order to balance the beam?

A gun is fired, the bullet weights 16 g. It moves at a speed of 112 m/s, this bullet gets stuck in a disk. The disk properties are as follows, 2.5kg and r=0.4 m. What is the angular speed of the disk after the bullet lodges into it.

A 200 g , 22-cm-diameter plastic disk is spun on an axle through its center by an electric motor. What torque must the motor supply to take the disk from 0 to 1500 rpm in 4.7 s ?

You are in your car A on the 407 driving at a constant velocity ~vA = (vA, 0, 0) and next to it another car (B) takes the exit ramp on one of Toronto’s huge exchangers to get onto the 404. For consistency we set the two cars to start at (0, 0, 0) at t = 0 and car B turns in the positive y direction. The exchanger can be seen as a quarter circle of radius R. 1. What are the components of the trajectory ~rA in the reference frame of the Earth? What are the components of the trajectory ~r 0 A and velocity ~v 0 A in the reference frame attached to car A? [1 mark] 2. What are the velocity and trajectory components of car B, ~vB and ~rB respectively, in the reference frame of the Earth? [3 marks] 3. What are the velocity and trajectory components of car B, ~v 0 B and ~r 0 B with respect to car A? [3 marks] 4. What is the condition to see car B from car A’s window at the same position (same x component)? [1 mark] 5. Express with vB and R the duration during which this condition holds. [2 marks]

Show that the tensor product of two positive operators is positive.

From the following techniques:

Thermal CVD (Chemical Vapor Deposition),

Metalorganic CVD,

Plasma-enhanced CVD,

Atomic Layer Deposition (ALD),

Plating,

Sol-gel,

Sputtering,

Thermal evaporation,

Electron beam evaporation,

Molecular Beam Epitaxy (MBE),

Laser ablation,

Ion plating,

choose one that is best suited for depositing

a) 100 nm Al coating on a rolled polymer foil having width of 1 m and length of hundreds of meters,

b) High purity 10 nm Au coating on a Si₃N₄ on Si substrate to be used as a contact,

c) Insulating 50 nm thick layer of oxide on a highly porous piece of material, which needs to be coated throughout,

d) 20 µm of zinc on a frame of a car.

Motivate your selections and discuss qualitatively the resulting film quality, productivity, cost, possible hazards and environmental issues.

You are working in a biotechnology company that specializes in the design of mass spectrometers with the team that develops the velocity selector. As part of the project design, you are in charge to solve the following problem. Molecules of mass 124u (u = 1.661×10−27 kg), have been ionized knocking out one electron, so its charge is ? = +?. The molecules, travelling horizontally, are accelerated until they reach a speed ?0 = 4.80 × 104 m/s, and then pass through a region between two horizontal electrode plates 2.50 cm long, separated a distance 2.00 cm. There is a vertical electric field of magnitude E pointing upwards, between the plates. After the molecules clear the region between the plates, they travel a horizontal distance ? = 1.50 cm (there is no electric field in this region) and must impact on a detector at vertical distance ℎ = 8.10 mm above the location they entered the plates (that is, the vertical displacement, from the time the molecules enter the region between the deflecting plates, until they hit the detector, is 8.10 mm). You must find the magnitude E of the electric field, to produce this result.

Make sure to:

• Draw a picture

• Include sufficient work.

• List any assumptions that may simplify the problem.

EXERCISE 1.2-3

Sensation Aberration-Free Imaging Surface. Determine the equation of a convex spherical (nonspherical) surface between media of refractive indexes n1 and n2 such that all rays (not necessarily paraxial) from an axial point P1 at a distance z1 to the left of the surface area image onto an axial point P2 at a distance z2 to the right of the surface [Fig. 1.2-12(a)]. Hint: In accordance with Fermat's principle the optical pathlengths between the two points must be equal for all paths.

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i have an assignment and i need the answer for this question from the book , "FUNDAMENTAL OF PHOTONICS" by B.E.A SALEH. I need solution urgently

Explain Intermodal and Intramodal dispersions that occur in optical fiber and derive
the expression for intermodal dispersion.