Which of the following best indicates the components of a vector that measures 30 m at 135°?

a)<21, 21> m

b)<-21, 21> m

c)<21, -21> m

d)<-21, -21> m

A student runs off of a diving platform with a speed of 2.5 m/s and hits the water 0.8 seconds later. What is the height of the platform?

Vector A has components A = <-2, 5> m/s and vector B has components B = <6, -2> m/s. What is the magnitude of vector C if C = A + B?

A student fires a bullet horizontally from a gun. Which statement is most accurate?

Which of the following is an example of a vector measurement?

A person driving through a field has velocity components that are 30 m/s west and 20 m/s south. What is the approximate direction of the overall velocity?

A student kicks a ball that is initially at rest on the ground. The ball leaves the student's foot with some velocity v at an angle θ. When the ball is at its maximum height, which statement is most accurate?

A proton has an initial velocity of 7.6 × 106 m/s in the horizontal direction. It enters a uniform electric field of 8800 N/C directed vertically.

a) Ignoring gravitational effects, find the time it takes the proton to travel 0.127 m horizontally. The mass of the proton is 1.6726 × 10−27 kg and the fundamental charge is 1.602 × 10−19 C . Answer in units of ns.

b)What is the vertical displacement of the proton after the electric field acts on it for that time? Answer in units of mm.

c) What is the proton’s speed after being in the electric field for that time? Answer in units of km/s.

An electron starts from rest 27.0 cm from a fixed point charge with Q = -8.00 nC .

How fast will the electron be moving when it is very far away?

------------------

Many chemical reactions release energy. Suppose that at the beginning of a reaction, an electron and proton are separated by 0.135 nm , and their final separation is 0.101 nm .

How much electric potential energy was lost in this reaction (in units of eV)?

---------------------------------------

A 0.21-F capacitor is desired. What area must the plates have if they are to be separated by a 3.2-mm air gap?

Robert Millikan is famous for his experiment which demonstrated that electric charge is discrete, or quantized. His experiment involved measuring the terminal velocities of tiny charged drops of oil in air between two plates with a known voltage applied. He timed hundreds of them traveling both up and down in order to mathematically rule out the effects of gravity and drag, since he had no way of measuring mass or diameter. His results showed that charge comes only in integer multiples of 1.6 10 19C. This is called the elementary charge. It is the charge on both electrons, negative, and protons, positive.
1. a. Where does charge excess charge reside on an object? Why?
b. Where is electric charge more concentrated on irregularly shaped objects?
c. How do lightning rods work?
d. Why does a stream of water bend toward a charged object?
e. What are the three methods of charging an object?

A ball is thrown straight up from the edge of the roof of a building. A second ball is dropped from the roof a time of 1.20 s later. You may ignore air resistance.

A) If the height of the building is 20.7 m , what must the initial speed be of the first ball if both are to hit the ground at the same time?

B) Consider the same situation, but now let the initial speed v0 of the first ball be given and treat the height h of the building as an unknown. What must the height of the building be for both balls to reach the ground at the same time for v0 = 8.65 m/s .

C) If v0 is greater than some value vmax, a value of h does not exist that allows both balls to hit the ground at the same time. Solve for vmax.

D) If v0 is less than some value vmin, a value of h does not exist that allows both balls to hit the ground at the same time. Solve for vmin.

) (Take eastward as the positive direction) Zachary, who is a runner, runs 8.30m/s westward for 12.0s. Zachary then turns around and runs 50.0m eastward toward the starting point in 30.0s. What is the Zachary’s a) total displacement b) total distance traveled c) explain the difference in your values for parts (a) and (b) d) average speed for the entire run e) average velocity for the entire run f) explain the difference in your values for parts (d) and (e)

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