A.) A 700- kg car collides with a 1300- kg car that was initially at rest at the origin of an x-y coordinate system. After the collision, the lighter car moves at 15.0 km/h in a direction of 30 o with respect to the positive x axis. The heavier car moves at 18 km/h at -41 o with respect to the positive x axis. What was the initial speed of the lighter car (in km/h)?

B.) What was the initial direction (as measured counterclockwise from the x-axis)?

I found the answer for A but can't seem to find the answer for B

A 2.00 mol sample of an ideal gas with a molar specific heat of CV = 5/2 R always starts at pressure 1.50 ✕ 10^5 Pa and temperature 350 K. For each of the following processes, determine the final pressure (Pf, in kPa), the final volume (Vf, in L), the final temperature (Tf, in K), the change in internal energy of the gas (ΔEint, in J), the energy added to the gas by heat (Q, in J), and the work done on the gas (W, in J) a.) The gas is heated at constant pressure to 460 K. b.) The gas is heated at constant volume to 460 K. c.) The gas is compressed at constant temperature to 200 kPa d.) The gas is compressed adiabatically to 200 kPa.

A bar of length ℓ lies on the ?̂-axis with its center at the origin. A proton sits on the ?̂-axis, a height of ℎ above the center of the bar. The bar carries a total charge of ?, which is distributed uniformly along its area.

a. Find the electric field vector experienced by the proton. I ask that you do solve this integral, though you may use any means necessary to do so (yes, including WolframAlpha).

b. Find the electric field vector experienced by the proton if the bar is infinitely long (but still “centered” on the origin).

A series circuit contains a 3.00-H inductor, a 2.40-μF capacitor, and a 25.0-Ω resistor connected to a 120-V (RMS) source of variable frequency. Find the power delivered to the circuit when the frequency of the source is each of the following.
(a) the resonance frequency
(b) one-half the resonance frequency
(c) one-fourth the resonance frequency
(d) two times the resonance frequency
(e) four times the resonance frequency

From your calculations, can you draw a conclusion about the frequency at which the maximum power is delivered to the circuit?

Calculate Brunt-Vaisala Frequency for a neutrally stable dry atmosphere

Many laws govern the physical universe (e.g. Newton's Universal Law of Gravity or Kepler's Laws of Planetary Motion) and can be expressed mathematically. Do you believe that mathematics is inherently part of the universe, or do you believe that mathematics is simply a tool we have developed to model behavior of objects in our universe? Another way of thinking of this issue is the following: why should the universe allow us to describe it mathematically?

Julie throws a ball to her friend Sarah. The ball leaves Julie's hand a distance 1.5 meters above the ground with an initial speed of 13 m/s at an angle 52 degrees; with respect to the horizontal. Sarah catches the ball 1.5 meters above the ground.

1.What is the maximum height the ball goes above the ground?

2. After catchingt he ball, Sarah throws it back to Julie. The ball leaves Sarah's hand a distance of 1.5 meters above the grounf, and is moving with a speed of 10m/s when it reaches maximum height of 8m above the ground. Wat is the speed of the ball when t leaves Sarah's hand?

3.How high above the ground will the ball be when it gets to Julie?

Consider an object with a mass of 3.5 kg located at R1 = (0.0 m, 2.5 m), another object with a mass of 3.5 kg located at R2 = (1.5 m, 1.5 m), and a third object with a mass of 8.5 kg located at R3 = (– 2.5 m, 2.5 m), and a fourth object with a mass of 5.0 kg located at R4 = (2.5 m, 0.0 m). Calculate the center of mass of this group of four objects. Give your answer in the form Rcm = (xcm, ycm) and with 2 significant figures.

Block 1, with mass m₁ and speed 3.5 m/s, slides along an x axis on a frictionless floor and then undergoes a one-dimensional elastic collision with stationary block 2, with mass m₂ = 0.67m₁. The two blocks then slide into a region where the coefficient of kinetic friction is 0.57; there they stop. How far into that region do (a) block 1 and (b)block 2 slide?

A steam pipe is covered with 1.50-cm thick insulating material of thermal conductivity of 0.200 cal/cm · °C · s. How much energy is lost every second when the steam is at 240°C and the surrounding air is at 20.0°C? The pipe has a circumference of 800 cm and a length of 50.0 m. Neglect losses through the ends of the pipe.

A proton and an alpha particle (q=+2e,m=4u) are fired directly toward each other from far away, each with an initial speed

of 0.014 c .

Part A

What is their distance of closest approach, as measured between their centers?

Express your answer to two significant figures and include the appropriate units

How can discuss the subject (the nearly free electron approximation)? and tight-binding approximation?

Suppose that the average U.S. household uses 13600 kWh (kilowatt-hours) of energy in a year. If the average rate of energy consumed by the house was instead diverted to lift a 2350 kg car 11.3 m into the air, how long would it take?

Using the same rate of energy consumption, how long would it take to lift a loaded 747, with a mass of 4.10 × 105 kg, to a cruising altitude of 9.67 km?

A 19.0-kg child on a 4.00-m-long swing is released from rest when the ropes of the swing make an angle of 35.0° with the vertical.

(a) Neglecting friction, find the child's speed at the lowest position.
m/s

(b) If the actual speed of the child at the lowest position is 3.30 m/s, what is the mechanical energy lost due to friction?
J