Two canoeists start paddling at the same time and head toward a small island in a lake, as shown in the figure (Figure 1) . Canoeist 1 paddles with a speed of 1.40m/s at an angle of 45 ? north of east. Canoeist 2 starts on the opposite shore of the lake, a distance of 1.5 km due east of canoeist 1.

a-

In what direction relative to north must canoeist 2 paddle to reach the island?

Express your answer using two significant figures.

b-

What speed must canoeist 2 have if the two canoes are to arrive at the island at the same time?

Express your answer using two significant figures.

A spherical raindrop 1.9 mm in diameter falls through a vertical distance of 5000 m. Take the cross-sectional area of a raindrop = ?r², drag coefficient = 0.45, density of water to be 1000 kg/m³, and density of air to be 1.2 kg/m³.

Calculate the speed a spherical raindrop would achieve falling from 5000 m in the absence of air drag.

What would its speed be at the end of 5000 m when there is air drag?

An object is 32cm in front of a convex mirror with a focal length of -19cm .Locate the image?

Is the image upright or inverted?

An object is 15cm in front of a concave mirror with a focal length of 22. Locate the image.cm.

Is the image upright or inverted?

One cylinder in the diesel engine of a truck has an initial volume of 600cm3 . Air is admitted to the cylinder at 25?C and a pressure of 1.0 atm. The piston rod then does 300J of work to rapidly compress the air.

Final temperature was calulated to be 610 degree celcius.

What is the final volume?

I wonder what were the main experiments that led people to develop the concept of wave function collapse? (I think I am correct in including the Born Rule within the general umbrella of the collapse paradigm.) Are there any instances where cases once thought to be examples of collapse have since been explained as the normal time-evolution of the wave function?

EDIT: I'm going to have to make an objection to Ron Maimon's very excellent answer about particle tracks as evidence of collapse. I've been waiting for someone to suggest what I personally have always considered the prototype of the wave function collapse, namely the appearance of flecks of silver on a photographic plate when exposed to the light of a distant star. This has the essential elements of collapse in a way that ordinary photographic exposures do not. The mere appearance of dots on a photographic plate does not signal the collapse of anything: it is readily explainable as a consequence of the rate of silver-bromide reduction being proportional to light intensity. It is only when the intensity becomes so very low that the time taken to accumulate enough energy for a single conversion becomes unreasonable that we must consider the explanation of wave function collapse.

The tracks in the cloud chamber do not demonstrate this phenomenon since the energy needed for the creation of the tracks is already available in the supersaturated gas. It is not necessary for the incoming particle to supply energy for the creation of the track, so there is no need to collapse its wave function. The straightness of the tracks is explained by Mott as an ordinary consequence of time-evolution of the wave function. There is no experimental proof that a single "particle" cannot be responsible for multiple tracks in the cloud chamber, because the tracks are not tagged according to which particle created them.

1. think about the modes of substances in the gas phase and explain why potential energy is included in the thermal energy of some substances in the gas phase, but not in other substances in the gas phase.

2. PE= E-bond + (1/2)E-thermal             and           KE = (1/2)Ethermal

when a monatomic solid/liquid turns into a gas, what are the PE and KE equal to then?

Derive/show the second order differential equation that describes the system and resonance.

Two identical blocks are placed 5 m apart. Each has a mass of 5 kg, is electrically neutral, and is made entirely of copper. Note: One copper atom has a mass of 1.055

I don't fully understand what would happen if we could travel at the speed of light. But I saw somewhere here that it would mean events happen out of order. But why is this a problem. It is said that cause has to happen before the effect, but why does this have to be linear?

And why is it that the speed of light is the maximum? I take it that light (photons?) are massless, so why can't they travel faster?

I am learning sailing on a 5m catamaran (Nacra 5). I am familiar with basic aerodynamics and the physics of the sail and keel.

We learned that when sailing closed hauled, too tight a mainsail tends to bring the boat up to the wind. And that the opposite is true for the jib. For example, one may steer up to the wind to come about, using the mainsail alone, by trimming it tight.

My question is why the trimmed mainsail in the above setup gives a larger torque.

This also seems opposed to the rule: "The more the mainsail is sheeted out the more the boat tends to come up.", as explained in http://www.sailtheory.com/mandf.html#sailsteering

Edit:

To my understanding, there are several possible competing effects involved:

(1) Effects that tend to INCREASE the mainsail torque to head up:

(1A) The direction of the sail force becomes more perpendicular to the boat. This increases the heeling torque. Since heeling motion happens faster than turning, the boat will heel more. This moves the sail force out, which increases the lever arm and the torque to head up. see diagram in: http://www.sailtheory.com/mandf.html#hellingstuur

(1B) The sail force moves backwards since the sail is stretched backwards. This increases the lever arm and the torque.

(2) Effects that tend to DECREASE the mainsail torque to head up:

(2A) The direction of the sail force becomes more perpendicular to the boat. Assuming that the force is perpendicular to the sail, and that the center of rotation is between the mast and the center of force, one sees that pulling the sail in, reduces the torque to head up, as can be seen in the following diagram:

diagram of the sail force torque

As Theta gets smaller, the torque Tau is reduced. This is opposed to what is stated in some of the answers below.

(2B) The sail force is reduced since the sail was pulled beyond its optimal angle of attack, thus losing lift and reducing torque.

(2C) Due to (2B) heeling torque is also decreased. With a similar reasoning to (1A) this decreases the lever arm and torque.

(2D) The sail force moves forward since the aft part of the sail is too flat and stalls. This shortens the lever arm and reduces torque. This is described in http://www.sailtheory.com/mandf.html#sailsteering

We know from reality that 1A+1B > 2A+2B+2C+2D. Considering heeling alone, we also know that 1A > 2C. It remains to be explained why in general this is the case.

Consider a rock that is thrown off a bridge of height 68 m at an angle ? = 22

A certain supernova remnant in our galaxy is an expanding spherical shell of glow-ing gas. The angular diameter of the remnant, as seen from Earth, is 22.0 arcsec. The parallax of the remnant is known to be 4.17 mas from space telescope measurements.Compute its distance in parsecs and radius in astronomical units.

A 2.50 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 300 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). (Due to the nature of this problem, do not use rounded intermediate values in your calculations—including answers submitted in WebAssign.)

(a) The gas is heated at constant pressure to 405 K.

P_f =_______ kPa

V_f =_______ L

T_f =_______ K

ΔE_int=_______ J

Q =_______ J

W =_______ J

(b) The gas is heated at constant volume to 405 K.

P_f =_______ kPa

V_f =_______ L

T_f =_______ K

ΔE_int=_______ J

Q =_______ J

W =_______ J

(c) The gas is compressed at constant temperature to 200 kPa.

P_f =_______ kPa

V_f =_______ L

T_f =_______ K

ΔE_int=_______ J

Q =_______ J

W =_______ J

(d) The gas is compressed adiabatically to 200 kPa.

P_f =_______ kPa

V_f =_______ L

T_f =_______ K

ΔE_int=_______ J

Q =_______ J

W =_______ J

A bumper car with mass m₁ = 117 kg is moving to the right with a velocity of v₁ = 4.1 m/s. A second bumper car with mass m₂ = 98 kg is moving to the left with a velocity of v₂ = -3.2 m/s. The two cars have an elastic collision. Assume the surface is frictionless. What is the velocity of the center of mass of the system What is the initial velocity of car 1 in the center-of-mass reference frame? What is the final velocity of car 1 in the center-of-mass reference frame? What is the final velocity of car 1 in the ground (original) reference frame? What is the final velocity of car 2 in the ground (original) reference frame? In a new (inelastic) collision, the same two bumper cars with the same initial velocities now latch together as they collide. What is the final speed of the two bumper cars after the collision?