1.Consider a satellite of the earth in a circular orbit of radius R. Let M and m be the mass of the earth and that of the satellite, respectively. Show that the centripetal acceleration of the satellite is a_R = -(v^2/R)*(r/r) where v = |v| is the magnitude of the velocity V and r/r is a unit vector in the radial direction.

2.Using Newton's second low of motion and the law of universal gravitation, determine the speed v=|V| and the angular speed w for the circular orbit.

3.For two satellites in two different circular orbits with radii R1 and R2, respectively, prove kepler's second and third laws for this special case.

Provide the rationale for the use of thermal remote sensing in water pollution detection.

Present the advantage of Forward-Looking Infrared (FLIR) systems.

Why can SAR imagery be used for the detection of oil spill in the sea surface?

Provide the rationale for SAR imagery be used in the estimation of sea surface salinity.

A bullet is shot horizontally and becomes embedded in a large block, which is initially at rest on a horizontal surface. How far will the block slide before stopping? The mass of the bullet is 12.6 g, the mass of the block is 9.8 kg, the bullet's impact speed is 710 m/s, and the coefficient of kinetic friction between the block and the surface is 0.220. (Assume that the block does not spin after being hit with the bullet.)

1. **A crate with a mass of 45 kg is suspended from a massless rope that runs vertically upward over a light pulley. The other end of the rope is connected to a 35 kg crate, which lies on a tabletop. The coefficients of the kinetic friction and the static friction between the crate and the surface are 0.3 and 0.5 respectively. An applied force, F, pulls the 35 kg crate to the right.

1. In the first case, the applied force is just sufficient to keep the crates from sliding. Draw clearly labeled free-body diagrams for each crates including all forces drawn to scale.
2. How much force would need to be applied in this first case?
3. In the second case, the 35 kg crate is sliding to the right with a constant velocity. Draw clearly labeled free-body diagrams for each crate including all forces drawn to scale.
4. How much force would need to be applied in this second case?
5. In the third case, the 35 kg crate moves to the right at a constant acceleration of 0.5 m/s². Draw clearly labeled free-body diagrams for each crates including all forces drawn to scale. In this instance, draw the direction of acceleration next to each diagram.
6. How much force would need to be applied in the third case.

What is the dependence of debye wave vector on density?

ESSAY PART:

A group of students of students wants to build an apparatus that produces a mirage of an object. For this purpose, they need to know the radius of curvature of the concave mirror they are using. Please explain how they can achieve their goal? Make sure to indicate variables, equipment necessary and possible procedure. (10pts) Also on the space labeled Experimental setup sketch your apparatus.

Experimental Setup: (5 pts)

1. The students completed their corresponding measurements and obtained the following data:

Complete the above table by manipulating the data so that you are able to determine the focal length of the mirror. (20pts)

2. Graph your manipulated data. (20 pts)

3. Write the mathematical equation describing the relationship. Explain the physical meaning of the slope and the y-intercept. (30 pts)

Mathematical Equation: ____________________    Meaning of the Slope:             Meaning of the y-intercept:

4. Determine the radius of curvature of the mirror: (5 pts)
5. The mirror has a radius of curvature of 14.8 cm. Determine the percentage error of the experiment. (5 pts)

Select all the features Jupiter and Saturn have in common.

How does growth occur as a result of knowing our value?

What qualities in people do you admire most?

What are the data elements used to describe an object's position and motion? How can satellite orbits be classified (i.e. put into categories)?

Object A is moving due east, while object B is moving due north. They collide and stick together in a completely inelastic collision. Momentum is conserved. Object A has a mass of mA = 17.0 kg and an initial velocity of v0A = 8.10 m/s, due east. Object B, however, has a mass of mB = 29.0 kg and an initial velocity of v0B = 5.20 m/s, due north. Find the magnitude of the final velocity of the two-object system after the collision.

A particle that has a charge of 7.6 μC moves with a velocity of magnitude 4 × 105 m/s along the +x axis. It experiences no magnetic force, although there is a magnetic field present. The maximum possible magnetic force that the charge with the given speed could experience has a magnitude of 0.310 N. Find the magnitude and direction of the magnetic field. Note that there are two possible answers for the direction of the field.

An incompressible fluid is flowing through a vertical pipe with a constriction. The wide section is 2.00 cm in diameter and is at the top of the pipe. The pressure of the fluid in the wide section at the top is 200 kPa. The velocity of the fluid in the wide section is 4.00 m/s. The narrow section is located 4.00 m below the wide section. What is the diameter of the narrow section for the pressure of the fluid in the narrow section to equal the pressure in the wide section? (density of the fluid is 1,000 kg/m³)

A light plane attains an airspeed of 480 km/h. The pilot sets out for a destination 780 km due north but discovers that the plane must be headed 19.0

A major league pitcher stands on the pitching mound 60ft 6in from home plate throws a fastball at 105 mph. Assume both the batter and pitcher are the same height (6ft 6in) and the ball is released 55 inches above the ground when thrown horizontal.

a. How far will a 340 gram baseball travel before hitting the ground?

b. How high is the ball above the ground when it passes over home plate?

c. How long does it take to reach home plate?

Now let’s look at what happens when the ball is hit, using the setup from the last problem. When hit the ball’s speed is an average of 30% faster and leaves the bat at a 5 degree angle.

(a) How high is the ball when it passes the pitching mound?

(b) How far will the ball travel?

You drop a 1.70 kg book to a friend who stands on the ground at distance D = 12.0 m below. If your friend's outstretched hands are at distance d = 1.60 m above the ground (see the figure), (a) how much work Wg does the gravitational force do on the book as it drops to her hands? (b) What is the change ΔU in the gravitational potential energy of the book-Earth system during the drop? If the gravitational potential energy U of that system is taken to be zero at ground level, what is U (c) when the book is released and (d) when it reaches her hands? Now take U to be 100 J at ground level and again find (e) Wg, (f ) ΔU, (g) U at the release point, and (h) U at her hand