Thread: Related Rates

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

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)>

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?

The planes momentum is:

,

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



Part (a) we have the speed is constant:

,

so:

.

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



Part (b) at 1hr we have the mass of the aircraft and ice is , the speed is ,
, and , so:



RonL