tis question..?

**xiaoz** · June 21st 2006, 03:19 AM

can anyone help mi wif tis..?

**Quick** · June 21st 2006, 03:35 AM

Originally Posted by xiaoz

can anyone help mi wif tis..?

Originally Posted by some stupid assignment

The time, $T$ minutes, taken by the moon to eclipse the sun totally is given by the forumula $T=\frac{2}{v}\left(\frac{Rd}{D}-r\right)$ where $R$ and $r$ are the radii, in km, of the sun and moon respectively; $D$ and $d$ are the distances , in km, of the sun and moon respectively from the earth and $v$ is the speed of the moon in km/min.

(i) Express $d$ in terms of $D$ , $R$ , $r$ and $v$

This is Simple Algebra, all you need to do is solve for d...
$T=\frac{2}{v}\left(\frac{Rd}{D}-r\right)$ divide both sides by $\frac{2}{v}$

$T\frac{v}{2}=\left(\frac{Rd}{D}-r\right)$ get rid of paranthesis..

$T\frac{v}{2}=\frac{Rd}{D}-r$ Add $r$ to both sides..

$T\frac{v}{2}+r=\frac{Rd}{D}$ multiply both sides by $D$

$DT\frac{v}{2}+Dr=Rd$ finally, divide both sides by $R$

$\frac{DT\frac{v}{2}+Dr}{R}=d$ simplify

$\frac{DTv}{2R}+\frac{Dr}{R}=d$ and that is what $d$ is.

Originally Posted by some stupid assignment

(ii) Calculate the distance from the earth to the moon...

All you need to do is substitute the given numbers into the equation that I gave you, and then you'll know!

**Soroban** · June 21st 2006, 03:58 AM

Hello, xiaoz1

Part (a) cn b solvd wif just algebra . . .

We hav: . $\frac{2}{v}\left(\frac{Rd}{D} - r\right)\;=\;T$

Mult by $v:\;\;2\left(\frac{Rd}{D} - r\right)\;=\;vT$

Div by $2:\;\;\frac{Rd}{D} - r\;=\;\frac{1}{2}vT$

Add $r:\;\;\frac{Rd}{D}\;=\;\frac{1}{2}vT + r$

Mult by $D:\;\;Rd\;=\;D\left(\frac{1}{2}vT + r\right)$

Div by $R:\;\;d\;=\;\frac{D}{R}\left(\frac{1}{2}vT + r\right)$

an (b) is arithmetic, can b done wif yr calculator

**Quick** · June 21st 2006, 04:17 AM

Originally Posted by Quick Rocks :)

(b) The wheel of a lorry travelling at 90km/h makes 8 revolutions per second. What is the diameter of the wheel in metres?

The wheel makes 8 revolutions per second, therefore it makes 28,800 revolutions per hour. Those 28,800 revolutions push it 90km, so each revolution pushes it $90\div28,800=0.003125$

That means the circumference of the wheel is 0.003125, and the diameter is of course the circumference divided by pi

$d=c\div \pi$ so I'm trusting you can find it from here.

**xiaoz** · June 21st 2006, 04:25 AM

omg.. i cannot figure out 11(a) ii

**Quick** · June 21st 2006, 08:26 AM

Originally Posted by xiaoz

may i no 11(aii) how to do ?

xiaoz, maybe it will help if I write out what the variables mean,

$\frac{DTv}{2R}+\frac{Dr}{R}=\text{The Distance From the Moon to the Earth}$

$D=\text{The Distance Between the Sun and the Earth}$

$T=\text{The Time it Takes to Totally Eclipse the Sun}$

$v=\text{The Speed of the Moon}$

$R=\text{The Radius of the Sun}$

$r=\text{The Radius of the Moon}$

The book gave you all the numbers, so all you need to do is substitute them into the equation above.

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