Answer:
h'=0.25m/s
Explanation:
In order to solve this problem, we need to start by drawing a diagram of the given situation. (See attached image).
So, the problem talks about an inverted circular cone with a given height and radius. The problem also tells us that water is being pumped into the tank at a rate of
. As you may see, the problem is talking about a rate of volume over time. So we need to relate the volume, with the height of the cone with its radius. This relation is found on the volume of a cone formula:

notie the volume formula has two unknowns or variables, so we need to relate the radius with the height with an equation we can use to rewrite our volume formula in terms of either the radius or the height. Since in this case the problem wants us to find the rate of change over time of the height of the gasoline tank, we will need to rewrite our formula in terms of the height h.
If we take a look at a cross section of the cone, we can see that we can use similar triangles to find the equation we are looking for. When using similar triangles we get:

When solving for r, we get:

so we can substitute this into our volume of a cone formula:

which simplifies to:


So now we can proceed and find the partial derivative over time of each of the sides of the equation, so we get:

Which simplifies to:

So now I can solve the equation for dh/dt (the rate of height over time, the velocity at which height is increasing)
So we get:

Now we can substitute the provided values into our equation. So we get:

so:

Answer : <em>Her weight is lower on Venus because the acceleration due to gravity is lower.</em>
Explanation :
Venus is also called as Earth's twin. This is because both the mass and the size of Earth and Venus are almost same. The acceleration due to gravity on earth is
while on Venus is
.
So, when Shari measure her weight on Venus she found her weight is lower on Venus. This is because the acceleration due to gravity is lower on the surface of Venus as compared to the Earth.
Since, 
i.e. weight depends on g.
<em>So, correct prediction is (b)</em>
For this case we have that by definition, the momentum equation is given by:

Where:
m: It is the mass
v: It is the velocity
According to the data we have:

Substituting:

On the other hand, if we clear the variable "mass" we have:

According to the data we have:

Thus, the mass is 
Answer:

Answer:
The velocity with which the mass will hit the floor is 
Explanation:
If the tension in the string is
, for
we have
,
and for the mass

From these equations we solve for
and get:

The kinematic equation

gives the final velocity
of a particle, when its initial velocity was
, and has traveled a distance
while undergoing acceleration
.
In our case
(the initial velocity of the particles is zero)

which gives us



which is the velocity with which the mass
will hit the floor.