Q. what is the difference between Black-litterman and Stutzer’s 2004 optimisation approach ?

A helicopter flying over a hard-to-reach area had an accident. The team of recatists know that the area where the plane fell has the form given by f(x,y) = xsiny, the last position given by the plane was in (3,0), they also know that the direction with which the helicopter went was determined by a normal vector to the parabola y = x^2 at the point (1,1). Find the speed with which the helicopter was going in the direction indicated so that the group of rescuers can make an estimate of the location of the aircraft.

Question 3

1. The electronic structure of atoms and molecules may be investigated using photoelectron spectroscopy. An electron in a photoelectron spectrometer is accelerated from rest by a uniform electric field to a speed of 420 km s⁻¹ in 10 µs. Determine the kinetic energy of the electron?

Question 4

1. The electronic structure of atoms and molecules may be investigated using photoelectron spectroscopy. An electron in a photoelectron spectrometer is accelerated from rest by a uniform electric field to a speed of 420 km s⁻¹ in 10 µs. Determine the magnitude of the work done on the electron.

10 points

Question 5

1. The most probable distance of an electron from the nucleus in the lowest energy state of a hydrogen atom is called the Bohr radius: a₀ = 52.9 pm. What is the electrostatic potential energy of interaction between the nucleus and the electron at this separation?

10 points

Question 6

1. At sea level, where the pressure was 104 kPa and the temperature 21.1 °C, a certain mass of air occupied 2.0 m³. To what volume will the region expand when it has risen to an altitude where the pressure and temperature are 880 Pa and −52.0 °C, respectively?

Question 7

1. A gas mixture is used to simulate the atmosphere of another planet consists of 320 mg of methane, 175 mg of argon, and 225 mg of nitrogen. The partial pressure of nitrogen at 300 K is 15.2 kPa. Calculate the volume of the mixture.

10 points

Question 8

1. Using the same given provided in question #7, calculate the total pressure of the mixture.

10 points

Question 9

1. The composition of planetary atmospheres is determined in part by the speeds of the molecules of the constituent gases because the faster-moving molecules can reach escape velocity and leave the planet. Calculate the mean speed of CH₄ molecules at 77K and 1500K.

Question 10

1. Please calculate the pressure exerted by 1.0 mol C₂H₆ behaving as a van der Waals gas when it is confined under the following condition at 1000 K in 100 cm³.

A metal sphere of radius a has a uniform (free) charge density σ_f on its surface. The permittivity of the dielectric region surrounding the sphere varies as , where r is the radial coordinate.

1. (1 pts) Determine the polarization P and electric field intensity E inside the sphere.
2. (3 pts) Determine the polarization P and electric field intensity E in the dielectric.
3. (5 pts) Calculate all bound charge densities, ρ_b and σ_{b. Is the dielectric homogeneous?}
4. (1 pts) Test whether the electric field intensity E in the dielectric is conservative.

Four equally charged particles with charge q are placed at the corners of a square with side length L, as shown in the figure below. A fifth charged particle with charge Q is placed at the center of the square so that the entire system of charges is in static equilibrium. What are the magnitude and sign of the charge Q? (Use any variable or symbol stated above as necessary.) magnitude Q =

The speed of waves on a string is 97 m/s. If the frequency of standing waves is 485Hz, how far apart are the two adjacent nodes?

Two sig figs and proper units

Part B: Ballistic Pendulum

The questions n the very bottom is pertaining to a lab over projectile motion and its asking to use equations on the bottom to find velocity. Below are the procedures of the lab and the necessary data to find initial velocity.

7. Place the ball in the launcher and cock the gun until the spring is locked in the same position as used for the previous part. Fire the gun. The ball will enter the catcher in the pendulum, which will swing up and return. A slider indicates the maximum angle by which it had moved. Repeat this procedure five times and obtain the average. Use the average angle and the length of the pendulum L (distance from pivot to its center of mass) to obtain the vertical distance ‘h’ moved by the center of mass of the pendulum+ball. (You will need to do some trigonometry to get ‘h’)
8. In some instruments, as the pendulum swings up, it comes to rest on a curved rack. For this instrument, record the vertical distance between the base of the apparatus and the center of mass of the pendulum+ball before it swings and after it stops. The difference is the vertical height ‘h’.
9. Use equations 1, 3 and 4 to obtain the initial speed of the ball. Compare this with the value obtained from part 1.

Calculate the average value for the vertical distance h the pendulum-ball system has risen after the collision. This is the difference between the height of CM at its highest point and that at its lowest point.

1  

Gain in Potential Energy = Loss in Kinetic Energy

Potential Energy at highest point =

Mass M of pendulum: 240 grams Mass m of ball: 64 g

Kinetic Energy at lowest point =        

Height h from angle and L= ?

Velocity V1 of pendulum as it starts to swing=?

Velocity Vo of ball=?

Calculate the average value for the vertical distance h the pendulum-ball system has risen after the collision. This is the difference between the height of CM at its highest point and that at its lowest point.

Using Energy balance and momentum conservation equations, calculate the initial velocity V₀ of the projectile.

1. Why is the steady state concentration gradient linear in equimolecular counter diffusion?

2. Explain why the dissolution of a crystalline particle in a solution can be speeded up by (a) stirring the solution and (b) by crushing the particle, from a mass transfer perspective.

1) In 2014 the Rosetta spacecraft, orbiting the comet 67P/Churyumov-Gerasimenko, measured the rotation period of the comet's nucleus at 12.404 h. By the time the Rosetta mission ended in 2016, the period had decreased by 21 min. Find the new rotation period, expressed in hours.

2) In Earth’s current epoch, the length of the day is some 86,400.002 ss.

If that were to increase to 86,400.0108 ss, how would you report the increase?

Express your answer with the appropriate units.

3) Add 3.13105 mm and 2.23103 kmkm .

Express your answer with the appropriate units.

4) Add 1.46 mm and 2.3 cmcm.

Express your answer in meters.

An object moves with constant acceleration 4.10 m/s² and over a time interval reaches a final velocity of 13.8 m/s.

(a) If its original velocity is 6.90 m/s, what is its displacement during the time interval?
m

(b) What is the distance it travels during this interval?
m

(c) If its initial velocity is

−6.90 m/s,

what is its displacement during this interval?
m

(d) What is the total distance it travels during the interval in part (c)?
m

Part A: What is the area of contact each tire makes with the road?

Part B: If the gauge pressure is increased, does the area of contact increase, decrease, or stay the same?

Part C: What gauge pressure is required to give an area of contact of 111 cm2cm2 for each tire?