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a) For an image that is in front of a mirror, is the imagedistancepositive or negative?
b) Given the image distance, what additional information isneededto determine the focal length? Explain.
c) For an inverted image is the image height positiveornegative?
d) Given the object and image heights and a statement as towhetherthe image is upright or inverted, what additionalinformation isneeded to determine the object distance?
e) A small statue has a height of 3.5 cm and is placed in front ofaconcave mirror. The image of the statue is inverted, 1.5 cmtall,and is located 13 cm in front of the mirror. Find the focallengthof the mirror.

a) The drawing shows a ray of light traveling throughthreematerials whose surfaces are parallel to each other. Therefractedrays (but not the reflected rays) are shown as the lightpassesthrough each material. Taking into account the relative sizesofthe angles of incidence and refraction, rank thematerialsaccording to their indices of refraction, greatest first.Providereasons for your rankings.
b) A ray of light strikes the a-b interface ata50.0^o angle of incidence. The index of refractionofmaterial a is n_a = 1.20. The anglesofrefraction in materials b and care,respectively, 45.0^o and 56.7^o. Findtheindices of refraction in these two media

I tried to solve this problem twice but i can't get the rightresults.

If a person of mass M simply moved forward with speed V, hiskinetic energy would be 1/2MV² . However, in addition topossessing a forward motion, various parts of his body (such as thearms and legs) undergo rotation. Therefore, his total kineticenergy is the sum of the energy from his forward motion plus therotational kinetic energy of his arms and legs. The purpose of thisproblem is to see how much this rotational motion contributes tothe person's kinetic energy. Biomedical measurements show that thearms and hands together typically make up 13.0% of a person's mass,while the legs and feet together account for 37.0% . For a rough(but reasonable) calculation, we can model the arms and legs asthin uniform bars pivoting about the shoulder and hip,respectively. In a brisk walk, the arms and legs each move throughan angle of about Â±30^o (a total of 60^o ) fromthe vertical in approximately 1 second. We shall assume that theyare held straight, rather than being bent, which is not quite true.Let us consider a 75.0 person walking at 5.00km/h having arms70.0cm long and legs 90.0cm long.

A)What is the average angular velocity of his arms and legs?

B)Using the average angular velocity from part A, calculate theamount of rotational kinetic energy in this person's arms and legsas he walks.

C)What is the total kinetic energy due to both his forwardmotion and his rotation?

D)What percentage of his kinetic energy is due to the rotationof his legs and arms?

If you want to help, you don't need to solve the whole problem.Just explain how to solve. If you understand or know how to solvethis problem, please help.

Consider a traveling wave described by the formula

$y_1(x,t) = A \sin(k x - \omega t)$ .

This function might represent the lateral displacement of a string, a local electric field, the position of the surface of a body of water, or any of a number of other physical manifestations of waves.

Part A

Which one of the following statements about the wave described in the problem introduction is correct?

ANSWER:

The wave is traveling in the

direction.
The wave is traveling in the

direction.
The wave is oscillating but not traveling.
The wave is traveling but not oscillating.

Part B

Which of the expressions given is a mathematical expression for a wave of the same amplitude that is traveling in the opposite direction? At time t=0

this new wave should have the same displacement as y_1(x,t)

, the wave described in the problem introduction.

ANSWER:

$A \cos (k x - \omega t)$
$A \cos (k x + \omega t)$
$A \sin (k x - \omega t)$
$A \sin (k x + \omega t)$

The principle of superposition states that if two functions each separately satisfy the wave equation, then the sum (or difference) also satisfies the wave equation. This principle follows from the fact that every term in the wave equation is linear in the amplitude of the wave.

Consider the sum of two waves , where is the wave described in Part A and is the wave described in Part B. These waves have been chosen so that their sum can be written as follows:

$y_{\rm s}(x,t) = y_{\rm e}(x) y_{\rm t}(t)$ .

This form is significant because , called the envelope, depends only on position, and depends only on time. Traditionally, the time function is taken to be a trigonometric function with unit amplitude; that is, the overall amplitude of the wave is written as part of .

Part C
Find and . Keep in mind that should be a trigonometric function of unit amplitude.

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Philosophy 2074F/G Lecture Notes - Categorical Imperative

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