Answer:
H = 34.43 m
Explanation:
Given that,
Initial speed of the object, u = 30 m/s
The angle of projection,
We need to find the maximum height reached by the object. Let it is H. Using the formula for maximum height reached by the projectile.
So, the maximum height reached by the object is 34.43 m.
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
