Derive Lens equation of two convex lenses (L1 and L2) separated by 5 cm in Air. Write down the System Matrix equation and define each matrix elements.

On a frictionless horizontal air table, puck A (with mass 0.255 kg ) is moving toward puck B (with mass 0.375 kg ), which is initially at rest. After the collision, puck A has velocity 0.117 m/s to the left, and puck B has velocity 0.650 m/s to the right.

What was the speed vAi of puck A before the collision?

Calculate ΔK, the change in the total kinetic energy of the system that occurs during the collision.

A length of 20-gauge copper wire (of diameter 0.8118 mm) is formed into a circular loop with a radius of 24.0 cm. A magnetic field perpendicular to the plane of the loop increases from zero to 18.0 mT in 0.20 s. Find the average electrical power dissipated in the process.

What will the temperature of the cosmic microwave background be when the average distances between galaxies are 1.7 times as large as they are today? (Hint: The peak wavelength of photons in the background will then also be 1.7 times as large as it is today.)

Come up with a few collision situations where you think the forces the two carts exert on one another will be of equal magnitude. Briefly describe these situations.

Come up with a few collision situations where you think the forces the two carts exert on one another will be of different magnitude. Briefly describe these situations.

Come up with a few situations where one cart is pushing or pulling the other and you think the forces the two carts exert on one another will be of equal magnitude. Briefly describe these situations.

Come up with a few situations where one cart is pushing or pulling the other and you think the forces the two carts exert on one another will be of different magnitude. Briefly describe these situations.

Radius of Moon's orbit is 240000 miles and period of revolution is 27 days, diameter of Earth is 8000 miles and the value of gravity on its surface 32 ft/sec2. Verify the statement that the gravitational force varies inversely proportional to square of distance.

A mass is launched up a ramp so that the velocity of the mass at the bottom of the ramp is 11.0 m/s. The coefficient of friction between the ramp and the mass is 0.27, and the ramp angle is 41 degrees. How far up the ramp will the mass slide?

Please try to explain how you get your answer.

You’re the infamous captain of a roving band of pirates and you recently captured a castle

full of treasures. Another band of marauding pirates are trying to storm your castle. You have

a single cannon that can fire cannon balls from over the castle walls and down to the ground

below. In order to successfully hit the pirates on the ground, you need to know the

typical

launch speed of cannon ball fired from your cannon.

To determine the launch speed of the cannon ball, you fire a cannon ball and observe that the

ball hits a target

R

meters away as measured from the base of castle’s wall. The cannon ball

is fired horizontally at a height of

h

meters above the ground. Using these data, determine the

cannon ball’s time of flight

t

and its launch speed

v

0

. Your answer for time of flight should be

expressed in terms of

h

and

g

and your answer for launch speed should be expressed in

h

,

g

,

and

R

only.

A long coaxial cable with a radius s carries a uniform line charge Q on its inner conductor and a uniform surface charge -Q on its outer conductor.

a) Sketch the situation including the electric field E inside and outside the cable.

b) Find the electric field inside and outside the cable.

c) Plot |E| as a function of the radius s.

Ball 1 has an inertia of 0.500 kg and ball 2 has an inertia of 0.600 kg . Ball 1 is moving away from you at 5.0 m/s, and you decide to throw ball 2 at it to make it go faster. The balls collide head-on, and the coefficient of restitution for the collision is 0.83. A- How fast must ball 2 be traveling in order to double the velocity of ball 1? Express your answer with the appropriate units. B- What is the initial relative velocity of the two balls? Express your answer with the appropriate units. C- What is their reduced inertia? Express your answer with the appropriate units. D-What percentage of the original kinetic energy is convertible? E-What are the final velocities of the two balls immediately after the collision? Enter your answers numerically separated by a comma.

An LRC series circuit consists of a 3.15 H inductor, a 6.36 ohm resistor, and a 5.48 microFarand capacitor. The combination is connected to an AC votage source that has a peak voltage of 147 V and an angular frequency of 441 rad/s. What is the peak voltage measured across the inductor?

A catapult launches a test rocket vertically upward from a well, giving the rocket an initial speed of 79.2 m/s at ground level. The engines then fire, and the rocket accelerates upward at 3.90 m/s² until it reaches an altitude of 1060 m. At that point its engines fail, and the rocket goes into free fall, with an acceleration of −9.80 m/s². (You will need to consider the motion while the engine is operating and the free-fall motion separately.)

(a) For what time interval is the rocket in motion above the ground?

(b) What is its maximum altitude?

(c) What is its velocity just before it hits the ground?

A 0.5-kg rock is thrown with a velocity of 6 meters per second from a height of 10 meters. What is the total energy? (Use g=10 m/s2. The answer will be in joules, but you DO NOT NEED to write the units

A 1.90-kg particle moves in the xy plane with a velocity of v with arrow = (4.00 i − 3.70 j) m/s. Determine the angular momentum of the particle about the origin when its position vector is r with arrow = (1.50 i + 2.20 j) m.