The horizontal and vertical components of the initial velocity of a football are 20m/s and 30 m/s respectively. Assume that after rising some height, the football returns back to the ground level.

1) what is the speed of the football at 3s after launch?

2) to what maximum height does the football rise?

3)What horizontal distance does the football travel during its flight?

Please show full explaination and steps for answer.

use the thin lens equation to explain why for a given screen-object distance there are two positions where the image is in focus

A person is seated in a swivel chair. The moment of inertia around the swivel point will be about 3.0 kg m2for the person and chair combined. If their "friend" starts to spin them, changing their rate of rotation from 1.5 rad/s to 2.0 rad/s in 2.5 s, the net torque being applied is:
a. 0.60nm
b. 1.1nm
c. 2.4nm
d. 3.8nm
e. none of these

A person is seated in a swivel chair. The moment of inertia around the swivel point will be about 3.0 kg m2for the person and chair combined. If their "friend" starts to spin them, producing an angular acceleration of 4.0 rad/s2 for 5.0 s, the net torque being applied is:
a. 0.75nm

b. 1.3nm
c. 2.4nm
d. 12nm
e. none of these.

A person is seated in a swivel chair. The moment of inertia around the swivel point will be about 3.0 kg m2for the person and chair combined. When spinning at 2.0 rad/s, they will be brought to rest by friction in the bearings which applies a net torque whose magnitude is a constant 1.3 n m. How long will it take for them to stop?

1. 0.51 s

2. 4.6s

3. 5.0s

4. 8.7s

5. none of these.

How many ways can you see that heat can transfer from the inside to the outside of your room on a cold day? List at least three and describe in detail how heat moves through the different kinds of materials (glass, brick, wood, insulation, etc.)—by conduction, convection or radiation. Which process do you suppose dominates?

A 85.3-kg climber is scaling the vertical wall of a mountain. His safety rope is made of a material that, when stretched, behaves like a spring with a spring constant of 1.16 x 103 N/m. He accidentally slips and falls freely for 0.757 m before the rope runs out of slack. How much is the rope stretched when it breaks his fall and momentarily brings him to rest?

A massless pan hangs from a spring that is suspended from the ceiling. When empty, the pan is 53 cm below the ceiling. If a 105 g clay ball is placed gently on the pan, the pan hangs 60 cm below the ceiling. Suppose the clay ball is dropped from the ceiling onto an empty pan. What is the pan's distance from the ceiling when the spring reaches its maximum length?

Robert has just bought a new model rocket, and is trying to measure its flight characteristics. The rocket engine package claims that it will maintain a constant thrust of 13.8 N until the engine is used up. Robert launches the rocket on a windless day, so that it travels straight up, and uses his laser range-finder to meaure that the height of the rocket when the engine cuts off is 21.2 m. He also measures the rocket\'s peak height, which is 25.7 m. If the rocket has a mass of 0.763 kg, how much work is done by the drag force on the rocket during its ascent?

Two infinitely long parallel rods carrying uniform charge density lambda are at a distance d from each other. Find the electric force on a particle of charge q_* located a distance d directly left of one of the rods. (Derive the formula using Gauss' Law)

**Convert all units to MKS**

1. In some collisions, KE is less after the collision than before. Since energy

cannot be lost, what happened to it? What could you do to show this is true?

2. A 2.00g bullet strikes a 2.00kg block hanging from a long cord. The bullet imbeds itself in the block causing the block with bullet embedded to swing upwards to a height of 50.0 cm above its original position.

A. What type of collision best describes the bullet striking the block?

B. Do a walk-through of the energy of the system starting just before the bullet strikes the block and continue until the block and bullet reach max height.

C. Find the velocity of the bullet before it collides with the block.

3. A 450g rubber ball is dropped from 2.0m above the floor. After the bounce, the ball only rises to a height of 1.5m above the floor.

A. Determine the change in momentum of the ball when it hits the floor and bounces up. (hint: either use motion equations or conservation of energy to determine the speed of the ball when it reaches the floor.)

B. Calculate the amount of heat generated when the ball hits the floor.

C. Explain how momentum is conserved when the ball collides with the floor.

Two capacitors C₁ = 3.2 ?F, C₂ = 13.5 ?F are charged individually to V₁ = 19.0 V, V₂ = 5.6 V. The two capacitors are then connected together in parallel with the positive plates together and the negative plates together.

1.Calculate the final potential difference across the plates of the capacitors once they are connected.

2.Calculate the amount of charge (absolute value) that flows from one capacitor to the other when the capacitors are connected together.

3.By how much (absolute value) is the total stored energy reduced when the two capacitors are connected?

The energy released in the most energetic hydrogen bombs is often expressed in terms of how much TNT it would take to create the same energy release. The energy content of a large H-bomb is often expressed in megatons (1 megaton = 1 million tons of TNT). In more commonly used units, a megaton corresponds to 4.2 x 1015 Joules of energy, where a Joule is the kinetic energy of a softly hit tennis ball.

Given that information, calculate how much energy was released when the KT impactor hit the Earth 65 million years ago. Express your answer in terms of how many megaton H-bombs it would take to produce the same amount of energy. The energy released corresponds to all of the original kinetic energy of the incoming asteroid, which was moving at an estimated speed of 50 km/sec. Assume that the asteroid was spherical and had a diameter of 12 kilometers and a density of 3000 kg/m3.

Remember that the mass m of a body is its density times it volume. And use the fact that the kinetic energy of a body moving at velocity v is ½mv2. (Youll have the answer in Joules if you use kilograms for mass and meters/sec for the velocity.)

(b) Consider a 1D lattice with a two atom basis with N+1 atoms in total.

a. How many normal modes of vibration are there?

b. Draw a dispersion diagram to illustrate these modes.

c. Describe the motion of the atoms at three key points on the dispersion curve for a longitudinal vibration.

d. How can you interpret the principal quantum number, nk, for the k th vibrational mode?

e. In which branches and regions of the dispersion curve is an electromagnetic wave most likely to interact with the lattice vibration? Explain your answer.

The intensity of reflection of various wavelengths of light projected onto the eye can be used to determine the thickness of the tear film that coats the cornea. The tear film and cornea have indices of refraction 1.331 and 1.373, respectively. When white light is incident on the cornea, strong reflected intensities appear at wavelengths (in air) of 480 nm and 520 nm, but no wavelengths between them. What is the thickness of the tear film?