IT'S >>>>> PHYSICS!

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1. When you look at a not so smooth surface, such as your desktop or counter top in your room, at an oblique angle, you can see reflections of objects; but you do not see reflections (or as clearly) when you look vertically down on the counter top. Why?

2. You are throwing a ball by bouncing it once to your friend who is standing on his desk. Suppose the ball does not loose any energy in bouncing, what is the fastest route for the ball to take?

3. A lifeguard is 3m from the edge of a swimming pool, when he sees a boy drowing, he wants to get to the boy as quickly as possible. He can run 1m/s and swim 0.8m/s and the boy is 4m from the edge as shown. What should his path be?
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3) Snell's Law (refraction)

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markr wrote:

3) Snell's Law (refraction)

Thanks for your reply. Do you mind expanding on that? Do you mean that the quickest route is the straight path from the life guard to the boy?

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Snell's law relates the sin of the angle to the speed of light (lifeguard) in the media (land/water).

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ok, how does that apply to the scenario? i really need help on this. thanks

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Re: IT'S >>>>> PHYSICS!

Gouki wrote:

.........
1. When you look at a not so smooth surface, such as your desktop or counter top in your room, at an oblique angle, you can see reflections of objects; but you do not see reflections (or as clearly) when you look vertically down on the counter top. Why?

The light coming from an oblique angle, bouncing of the surface which is, in effect, compressed, relative to the light source, and reflected to the eye, appears to the optic nerves as a 'shine' phenomina. Light on a more perpendicular angle onto the surface is more absorbed and scattered by the surface variations not rendering the same result.

2. You are throwing a ball by bouncing it once to your friend who is standing on his desk. Suppose the ball does not loose any energy in bouncing, what is the fastest route for the ball to take?

the most direct route is a straight line (something that does not actually exist - energy is never 'not lost'), striking the floor and bouncing up to the receiver in a 'straight line' forming a 90 degree angle at the floor between the line down, and the line up; the angles to the floor, reflecting the difference in altitude of the thrower, and the receiver.

3. A lifeguard is 3m from the edge of a swimming pool, when he sees a boy drowing, he wants to get to the boy as quickly as possible. He can run 1m/s and swim 0.8m/s and the boy is 4m from the edge as shown. What should his path be?

a life guard who thinks at a time like this is a fool who may as well be 'dead in the water'!

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The lifeguard is going to run in a straight line to the edge of the pool, then swim in a straight line to the boy. In your drawing, call the intersection of the orange lines 0 and the intersection of the orange and blue lines 4.

The lifeguard needs to choose X (0<=X<=4) such that he minimizes the time it takes to get to the boy.

Two triangles will be formed:
land triangle: 3, x, sqrt(3^2+x^2)
pool triangle: 4, (4-x), sqrt(4^2+(4-x)^2)

land time = sqrt(3^2+x^2) / 1
pool time = sqrt(4^2+(4-x)^2) / .8

The lifeguard needs to minimize sqrt(3^2+x^2) / 1 + sqrt(4^2+(4-x)^2) / .8 with respect to x.

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thank you both for your replies. BoGoWo, do you mind expanding on the first explanation? Do you mean the light wave is compressed? Wait, can photons be compressed? lol, sorry I have no idea.

markr, those equations are of great help, but I've come to a point where, I cannot find the minimum value of x because there are sqrts on the left hand side. =( very ... tedious. However, i tried to find the time it takes if the lifeguard were to go in a straight line, directly towards the boy, and the time came out to be slightly more than 9 sec. While the other paths that I used are more than that. *bedazzled*

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Gouki wrote:

thank you both for your replies. BoGoWo, do you mind expanding on the first explanation? Do you mean the light wave is compressed? Wait, can photons be compressed? lol, sorry I have no idea.................

no i was referring to a 'virtual compression' of the surface of the desktop, caused by the angle of vision; if the hills and valleys in the desktop which serve to diffuse the light when it is viewed 'head on' are seen from an obtuse angle, the eye only catches the rays which bounce off the topmost peaks of the 'hills', and the light falling into the valleys is obscured. Thus what is seen appears as a 'reflection'.

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Ligeguard

T=sqrt(3^2+x^2) / 1+sqrt(4^2+(4-x)^2) / .8

dT/dx=0=x/sqrt(3^2+x^2)-1/0.8*(4-x)/ sqrt(4^2+(4-x)^2)

0.8*x sqrt(4^2+(4-x)^2)=(4-x)sqrt(3^2+x^2)
square this
0.64*x^2(4^2+(4-x)^2)=(4-x)^2(3^2+x^2)
4^2*0.64x^2=(4-x)^2(3^2+0.36x^2)

Now solve for x (tedious)

Easier solution, take the relation
T=sqrt(3^2+x^2) / 1+sqrt(4^2+(4-x)^2) / .8
and look at x in the middle. Then compare to x at 1/4 and 3/4 the length. From there you should be able to step closer and closer to the minimum time

Rap

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excellent guys, keep the replies coming.

Rap - i tried your guess and check method. It appears that when the life guard runs to the 2m point along the 4m, and then swim directly towards the boy; would minimize the time. How would I explain this though, that I guessed and checked? markr suggested Snell's law, and yes it does look like refraction, but how do I begin explaining anything like that?

BoGoWo: I know it would be outrageous to ask this but, if you could explain just a bit more on "virtual compression" and how the light is "obscured" when reflected from the valleys, then I'd be a much happier man! =) Links to diagrams/ pictures would be philanthropic!

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more questions
2. Q. A long necked empty flask containing some chalk pieces is placed inside a large beaker full of water. When you look horizontally, you see the flask is larger than it really is, Explain.
3. Q. In question 2, if you look vertically down, the content of the flask shrinks, or even disappears. Explain.
USE RAY DIAGRAM:

8
9. Q. A small hole constitutes seeing. Explain.

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Re: IT'S >>>>> PHYSICS!

Gouki wrote:

All help will be appreciated

1. When you look at a not so smooth surface, such as your desktop or counter top in your room, at an oblique angle, you can see reflections of objects; but you do not see reflections (or as clearly) when you look vertically down on the counter top. Why?

2. You are throwing a ball by bouncing it once to your friend who is standing on his desk. Suppose the ball does not loose any energy in bouncing, what is the fastest route for the ball to take?

3. A lifeguard is 3m from the edge of a swimming pool, when he sees a boy drowing, he wants to get to the boy as quickly as possible. He can run 1m/s and swim 0.8m/s and the boy is 4m from the edge as shown. What should his path be?
pictures

Hey dude ain u in mr Kong's Class AHHAHAHA
neway -- this is AFTER its due, however if ur really an enthusiast you'd actually want the answer to this
neway, for the lifegaurd question, if u use snells law and actually draw out the diagram its pretty easy where
N is a constant and N = C/V
where C is the speed of light and V is the speed of light in that particular medium THEREFORE
you can let C = to the speed of lifegaurd on land and V as the speed o lifegaurd in water therefore N = 1.25 and i have no idea how u got 9 because i got 10 and the fastest route for the life gaurd to take would be to face to the left of the boy "the normal" at a minimum of 1m and a max of 4m, because the water "using snell's law" would cause him to slow down creating a "bend" or in this case a turn towards the "normal" or in this case the boy *hope this is right cuz if it ain, i fail wit u dawg*

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wrong question Sad

what others did you do.

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IT'S >>>>> PHYSICS!

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