Question

The distance fallen by a body, starting from a position of rest in a vacuum near the easrth's surface, is proportional to the square of the time occupied in falling. If a body falls 256 ft. in 4sec, how far will it fall in 11 sec?

Answer 1

@iGreen

Answer 2

@Supreme_Kurt

Answer 3

So... two things are in direct proportion here, what are they?

Answer 4

vacuum near the easrth's surface and square of the time occupied in falling...IDK

Answer 5

the DISTANCE and the square of the time lol

Answer 6

So... let's let y be the distance and t be the time.
What then is the square of the time? :)

Answer 7

16?

Answer 8

\(\large t^2\)
But yeah, in your first scenario, it's specifically 16 :D

Answer 9

if direct proportional , is it the same as multiply?

Answer 10

and inverse is division?

Answer 11

You got it backwards :)
a and b are directly proportional if their QUOTIENT (divide them) is a constant:
a / b = k

a and b are inversely proportional if their PRODUCT (multiply them) is a constant
ab = k

Got it? :)

Answer 12

lol ... its completely the opposite that i say haha

Answer 13

Okay, so, get that y is directly proportional to t^2

That is to say
\[\Large \frac{y}{t^2}=k\]
Now you just have to find k.

Can you do that?

Answer 14

k=16

Answer 15

so i will substitute the value of k?

Answer 16

That's right. So that means k is 16, and since it's constant, it's ALWAYS 16 ^^

So let's have it updated, shall we:
\[\Large \frac y{t^2}=16\]
Now, your task is to find the distance if it took 11 seconds to fall.
t is 11.
What is d? :P

Answer 17

What is y, rather, haha

Answer 18

1936

Answer 19

isnt it?

Answer 20

feet.
And good ^^

Answer 21

ty...wanna go another run?

Answer 22

It's all you, kid. :P

err.. Who ARE you, anyway? :/

Answer 23

im kaitou

Answer 24

lol

Answer 25

...unusual. But yeah, great, Kaitou,
so let's just get it on :D

Answer 26

i will just type it here?

Answer 27

Sure. Just know that the longer a thread gets, the more the lag :D

Answer 28

the maximum horsepower of the boiler which can be served by a chimney of given cross section area is proportional to the square root of the height of the chimney. For an installation of a certain type,210 horsepower correspond to a height of 81 ft. Find the horse power for a height of 64ft.

Answer 29

You and your proportions.

Well then, Kaitou-kun, read the problem thoroughly, and tell me which values are proportional, and again, whether they are DIRECTLY or INVERSELY proportional.

Hop to it :)

Answer 30

im only a 1st year highschool

Answer 31

*shrug*
From where? Because some evil schools force unbelievably hard maths even on first-years :P

Answer 32

A=square root of h

Answer 33

its direct proportional.....area is proportional to square root of height

Answer 34

is it correct?

Answer 35

Nope. Area is actually given.
What's directly proportional to the square root of the height is the horsepower :P

Now, set up your equation again, and leave the constant alone on one side, for simplicity.

Answer 36

horse power = k/ square root of height

Answer 37

No... I said keep the constant (k) alone on one side of the equation.

horse power / square root of height = k

Now solve for k ^^

Answer 38

k=horse/sq. rt of height

Answer 39

k= 23.333

Answer 40

where you from?

Answer 41

That's correct :D
Stick to \[\Large \frac{70}3\] though, I think it's easier ^^

Now, your task is to find the horse power when the height is 64 instead of 81 :)

Answer 42

186.64

Answer 43

More like 186.67
but I think you got the idea ^^

Answer 44

can you help me to pass my analytic too..sometimes

Answer 45

i got 5 problems more here

Answer 46

Doesn't matter how many problems, as long as you learn. You'll find that I'll be a little more passive as the problems progress :)
Now, you might want to open a new question, the lag on this one is directly proportional to the length of the thread ;)

Answer 47

the approximate speed of a stream of water, necessary to move a round object, is proportional to the product of the square roots of the object's diameter and specific gravity. If a velocity of 11.34ft per second in needed to move a stone whose diameter is 1 foot and specific gravity is 4, how large a stone with specific gravity 6 can be moved by a stream whose speed is 22.68 ft per second?

Answer 48

Okay, this is a bit wordy :D
Where is the proportion here?
What is proportional to what? ^^

Answer 49

speed, square root of diameter,gravity,velocity

Answer 50

speed and velocity....
for now, consider them the same (this isn't physics lol)
So speed, square root of diameter, square root of specific gravity.

Answer 51

Can you set up the equation?
Which values are proportional?

Answer 52

No...
Read the problem CAREFULLY.
And like I said, to keep yourself from confusion, leave ALL the variables on one side of the equation, so that the other side only has the constant k, which you have to find, at some point.

...proportional to the PRODUCT of the SQUARE ROOTS of the object's diameter and specific gravity.

Care to set your equation up again? ^_^

Answer 53

That's better. Now find k ^^

Answer 54

how can i know the speed ?

Answer 55

velocity is speed :)

Answer 56

k=5.67

Answer 57

ok thats enough for now. can you help me with my trgi/geom stuffs here

Answer 58

That's correct :D
Can I assume you can work it out from there? ^^

(PS I'll be happy to help you with your trig/geom, as long as you're satisfied with the help you got here in this algebra stuff)

Answer 59

divide 5600 into four parts proportional to 5:3:4:2. Find x,y,z under the given condition

Answer 60

Ahh. This is called Partitive proportion. Fun stuff :)

What the heck are x,y, and z, though?

Answer 61

idk lol, it says in the book im using now

Answer 62

just leave it.

Answer 63

Okay, so let's divide 5600 that way.
It's actually pretty easy, what we have to do is divide it into four parts in that proportion. While it may sound pretty daunting, here's how to do it.

First, add up the numbers in proportion. 5:4:3:2
What do you get?

Answer 64

14

Answer 65

Okay. Now divide 5600 by that number. :)

Answer 66

i got 400

Answer 67

That's right.
Now multiply 400 to each of 5:4:3:2
And you'll have your answer :)

Answer 68

haaaaaaaaaaaaaaa........ pretty easy lol

Answer 69

Math is easy :P

Answer 70

wait lets move

Answer 71

Two perpendicular chord divide a circle with radius of 13cm into four parts. If the perpendicular distances of both chords are 5 cm each from the center of the circel , find the area of the smallest part.

Answer 72

heh. Your questions get harder and harder :P
Let me see if I can remember how to do this

Answer 73

this question is the last problem in the chapter :D

Answer 74

@hartnn

Answer 75

https://answers.yahoo.com/question/index?qid=20100513063354AAYaKAs
check this out my friend

Answer 76

o.O

Answer 77

hartnn :D please help