Can someone please help me with the questions in the attachment. Thanks :)

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- Dec 18th 2005, 11:06 AMASE2Related Rates
Can someone please help me with the questions in the attachment. Thanks :)

- Dec 18th 2005, 01:17 PMCaptainBlack
Clearly we would be doing you no favours in just solving them

all for you, so I will do one example and if you have specific

problems with the others you can post the question, what you have

done and what the difficulty is.

*<usual warning about checking the working yourself>*

*<another sugestion-it might be worthwhile converting the units to*

*metres (m), kilograms (kg) and seconds (s)>*

Quote:

2.An airplane of mass 10^5 kg flies in a straight line while ice builds up

on the leading edges of its wings at a constant rate of 30kg/h.

a) At what rate is the planes’s momentum changing if it

is flying at a constant rate of 800 km/h?

(Momentum (p) is the product of an object’s mass and

velocity: p = mv)

b) At what rate is the momentum of the plane changing

at t = 1h if at that instant its velocity is 750 km/h and

is increasing at a rate of 20 km/h/h?

$\displaystyle p=m.v$,

so the rate of change of momentum (using the product rule) is:

$\displaystyle \frac{dp}{dt}=\frac{dm}{dt}.v + m. \frac{dv}{dt}$

Part (a) we have the speed is constant:

$\displaystyle \frac{dv}{dt}=0$,

so:

$\displaystyle \frac{dp}{dt}= \frac{dm}{dt}.v$.

We are told:$\displaystyle \frac{dm}{dt}=30\ \mbox{kg/hr}$, and $\displaystyle v=800\ \mbox{km/hr}$,

plugging these in (and leaving the units as they are):

$\displaystyle \frac{dp}{dt}= 30.800=24000\ \mbox{km.kg.hr^{-2}}$

Part (b) at 1hr we have the mass of the aircraft and ice is $\displaystyle 100,030 \mbox{kg}$, the speed is $\displaystyle 750 \mbox{km/hr}$,

$\displaystyle \frac{dm}{dt}=30\ \mbox{kg/hr}$, and $\displaystyle \frac{dv}{dt}=20 \mbox{km/hr^2} $, so:

$\displaystyle \frac{dp}{dt}= 30.750+100030.20=2023100\ \mbox{km.kg.hr^{-2}}$

RonL