Two boys are standing on a bridge 10 m above a stream. One boy throws a rock horizontally with speed of 5.0 m/s at exactly the s
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Answer:
Explanation:
This is a recoil problem, which is just another application of the Law of Momentum Conservation. The equation for us is:
which, in words, is
The momentum of the astronaut plus the momentum of the piece of equipment before the equipment is thrown has to be equal to the momentum of all that same stuff after the equipment is thrown. Filling in:
Obviously, on the left side of the equation, nothing is moving so the whole left side equals 0. Doing the math on the right and paying specific attention to the sig fig's here (notice, I added a 0 after the 4 in the velocity value so our sig fig's are 2 instead of just 1. 1 is useless in most applications).
0 = 90.0v - 2.0 and
2.0 = 90.0v so
v = .022 m/s This is the rate at which he is moving TOWARDS the ship (negative was moving away from the ship, as indicated by the - in the problem). Now we can use the d = rt equation to find out how long this process will take him if he wants to reach his ship before he dies.
12 = .022t and
t = 550 seconds, which is the same thing as 9.2 minutes
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
