A satellite of mass 200kg completes a circular orbit of the Earth in 120 minutes. A 400 kg satellite is then put into orbit at t
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The tank has a volume of , where
is its height and
is its radius.
At any point, the water filling the tank and the tank itself form a pair of similar triangles (see the attached picture) from which we obtain the following relationship:
The volume of water in the tank at any given time is
and can be expressed as a function of the water level alone:
Implicity differentiating both sides with respect to time gives
We're told the water level rises at a rate of at the time when the water level is
, so the net change in the volume of water
can be computed:
The net rate of change in volume is the difference between the rate at which water is pumped into the tank and the rate at which it is leaking out:
We're told the water is leaking out at a rate of , so we find the rate at which it's being pumped in to be
