Krissy throws a ball from a height of 2.00 m above the ground. She throws the ball with a speed of 3.00 m/s directed 50.0 degrees above the horizontal. Find: a.) the speed of the ball at landing b.) the time it takes the ball to land c.) the angle with which the ball impacts the ground d.) the horizontal range of the ball e.) the maximum height of the ball f.) the time it takes the ball to reach maximum height g.) the speed of the ball at maximum height *This physics uses trig and algebra to slove problems.

There are many natural occurring radioactive isotopes. Among them, Radon(222Rn), 40K and 14C are the most important ones.

a) Where are/ were these isotopes produced and come from? You can consult Wikipedia for this question and briefly describe where they come from

b) Consider a person of 70 Kg. 0.20% of the body mass is potassium and it is a vital nutrient. Natural potassium (mostly 39K and 41K) also contains 0.012% 40K with a half- life time of 1.3 billion years. 40K emits a β- of average energy of 58.5 keV in 89.3% of its decays and a 1.461 MeV γ-ray in 10.7% of the decays. How many of these high-energy γ-rays is generated in the person per second?

c) If you assume that all the energy from the electrons and γ-rays is absorbed in the body, what is the effective dose for the person in one year?

d) While nowadays 0.012% of all potassium is 40K, what was its share of all potassium 4.5 billion years ago, when the Earth formed?

A tugboat tows a ship with a constant force of magnitude F₁. The increase in the ship's speed during a 10 s interval is 4 km/h. When a second tugboat applies an additional constant force of magnitude F₂ in the same direction, the speed increases by 16 km/h during a 10 s interval. How do the magnitudes of F₁ and F₂ compare? (Neglect the effects of water resistance and air resistance.)
F₂ = ? F1

Four identical bowling balls are placed on the corners of a square drawn on the ground whose sides are each .2 meters long. If the mass of each ball is 4kg, a)What is the magnitude of the net gravitational force acting on one of the balls due to all others, b)what is the magnitude and direction of the resulting acceleration of that ball? Please give full steps so I can follow along. TIA

A non-conducting sphere of radius R centered at O contains a spherical cavity of radius R’ centered at O'. Let d be the displacement of O’relative to 0. Throughout the sphere, there is a uniform charge density rho_0 (except inside the cavity, which is uncharged). (a) Use the principle of superposition to write down an expression for E(r) everywhere. (b) Repeat (a) for the electric potential b(r).

Compute the total quantity of heat (both in Kcal and J) required to raise the temperature of 1.00 kg of ice at -10.0 degrees C to 1.00 kg of steam at 110.0 degrees C. Assume no loss of mass or heat in this process. Note that this will requires several computations that must be completely added up, and you must include all phase changes and use the correct specific heats.

An object is thrown vertically upward with an initial speed of 56.9 m/s. (Assume the object is thrown from ground level.)

(a) How high (in m) does it rise?

(b) How long (in s) does it take to reach this highest altitude?

(c) How long (in s) does it take to hit the ground after it reaches the highest altitude?

(d) What is its speed (in m/s) when it returns to the level from which it was initially released?

The following multipart problem asks you to derive a number of characteristics of an extrasolar planetary system. Assume that the planet has been detected by Kepler with the transit method, and that the transits are periodic (as shown below, a dip in the lightcurve indicates that a planet has moved in front of the star).

(a) The star has 3 times the mass of the sun (i.e., M∗ = 3.0M⊙) and the period of the transits are 2.0 Earth years (i.e, the orbital period of the planet around its star is twice the orbital period of the Earth around the sun Tp = 2.0T⊕). To make things interesting, let’s imagine that the planet is in an elliptical orbit with eccentricity e = 0.3. What is the perihelion of the extrasolar planet to it’s star in a.u.? (Remember that the radius of the Earth’s orbit around the sun is a⊕ = 1 a.u., it might help to eliminate some constants).

(b) If the star has its maximum emission (observed flux per unit wavelength interval) at a wavelength of λp,∗ = 250nm what is the temperature of the star T∗? (Hint: note that the sun has it’s peak emission λp,⊙ = 500nm and has a temperature of T⊙ = 5, 800K, use ratios!)

(c) If the star has twice the radius of the sun R∗ = 3.0R⊙, what is the luminosity of the star relative to that of the sun L∗/L⊙?

(d) Now, using the relative luminosity of the star to the sun, L∗/L⊙, from part (c), the relative distances of the Earth to the sun, d⊕, and the average distance of the planet to its star, dp calculate the no-greenhouse temperature of the planet as follows: First, assume that all of the properties of the atmosphere and the planet’s surface (i.e., the emissivity, absorptivity, pollution, etc.) are the same as those of the Earth. Also assume that the radius of the planet is equal to twice that of the Earth Rp = 2R⊙. Solve for the ratio of the temperature of the planet to that of the Earth (Tp = T⊙). Then, use the average temperature of the Earth T⊕ = 256K to find Tp. Do you want to live on this planet? (Note: the no- greenhouse temperature is that temperature for which the total power absorbed by the planet, equals the total power re-radiated into space assuming the planet is a perfect black-body)

two masses m1 = 4.70 kg and m2 which has a mass 50.0% that of m1, are attached to a cord of negligible mass which passes over a frictionless pulley also of negligible mass. If m1 and m2 start from rest, after they have each traveled a distance h = 2.90 m, use energy content to determine the following.

(a) speed v of the masses

(b) magnitude of the tension T in the cord

A hockey puck is given an initial velocity of 39.6 m/s along the ice. Find the speed of the puck 1.08 s later if the coefficient of kinetic friction between puck and ice is 0.618. (HINT: The result is independent of the mass of the puck.)

In what ways did Galileo' observations of Venus and Jupiter conflict with the prevailing view at the time?

A cylinder with a piston contains 0.300 mol of oxygen at 2.00×10⁵ Pa and 340 K . The oxygen may be treated as an ideal gas. The gas first expands isobarically to twice its original volume. It is then compressed isothermally back to its original volume, and finally it is cooled isochorically to its original pressure.

Find the work done by the gas during the initial expansion. W_initial =

Find the heat added to the gas during the initial expansion. Q_{initial =}

Find internal-energy change of the gas during the initial expansion.

Find the work done during the final cooling. W_final

Find the heat added during the final cooling; Q_final

Find the internal-energy change during the final cooling;

Find the internal-energy change during the isothermal compression.

A bicycle wheel is rotating at 41 rpm when the cyclist begins to pedal harder, giving the wheel a constant angular acceleration of 0.50 rad/s2

What is the wheel's angular velocity, in rpm, 9.0 s later?

Problem 26.49: Resolution of the eye, I.

Even if the lenses of our eyes functioned perfectly, our vision would still be limited due to diffraction of light at the pupil.

Part A

Using Rayleigh's criterion, what is the smallest object a person can see clearly at his near point of 22.5 cm with a pupil 2.25 mm in diameter and light of wavelength 498 nm ? (To get a reasonable estimate without having to go through complicated calculations, we'll ignore the effect of the fluid in the eye.)

Part B

Based upon your answer, does it seem that diffraction plays a significant role in limiting our visual acuity?

a block of mass 2.4 kg is sitting on a frictionless ramp with a spring at the bottom that has a spring constant of 490N/m the angle of the ramp with respect to the horizontal is 31 degrees

A.) the block starting from rest slides down the ramp a distance 78 cm before hitting the spring how far in cm is the spring compressed as the block comes to momentary rest?

B.) After the block comes to rest the spring pushes the block back up the ramp how fast in meters per second is the block moving right after it comes off the spring

C.) what is the change of the gravitational potential energy in joules between the original position of the block at the top of the ramp and the position of the block when spring is fully compressed?