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:
Gravitational field strength is the force experienced by a unit mass. Gravitational force is the amount of force acting on a body. It is the product of field strength times the mass under consideration. Gravitational pull is just a more colloquial name for gravitational force.
Explanation:
hope it helps u
Answer:
The angular velocity is 
Explanation:
From the question we are told that
The mass of wooden gate is 
The length of side is L = 2 m
The mass of the raven is 
The initial speed of the raven is 
The final speed of the raven is 
From the law of conservation of angular momentum we express this question mathematically as
Total initial angular momentum of both the Raven and the Gate = The Final angular momentum of both the Raven and the Gate
The initial angular momentum of the Raven is 
Note: the length is half because the Raven hit the gate at the mid point
The initial angular momentum of the Gate is zero
Note: This above is the generally formula for angular momentum of square objects
The final angular velocity of the Raven is 
The final angular velocity of the Gate is 
Substituting this formula


![\frac{1}{3} m_g L^2 w = m_r * \frac{L}{2} * [u_r - v_r]](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B3%7D%20m_g%20L%5E2%20w%20%20%20%3D%20%20%20%20m_r%20%2A%20%20%5Cfrac%7BL%7D%7B2%7D%20%2A%20%5Bu_r%20-%20v_r%5D)
Where
is the angular velocity
Substituting value
![\frac{1}{3} (4.5)(2)^2 w = 1.2 * \frac{2}{2} * [5 - 1.5]](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B3%7D%20%284.5%29%282%29%5E2%20%20w%20%20%20%3D%20%20%20%201.2%20%2A%20%20%5Cfrac%7B2%7D%7B2%7D%20%2A%20%5B5%20-%201.5%5D)



I really need these points thx a lot
Answer:
5880lb-ft of work is done
Explanation:
The length of the heavy rope is given as 60ft and the weight per length is 0.7lb/ft.
Therefore, the total weight of the heavy rope is
60×0.7 =42lb.
The work done in pulling the heavy rope to the top of the building is w = Fd.
Where
F is force is measured in pounds;42lb
d is distance through which the heavy rope is to be pulled measured in feet; 140ft
w= 42lb×140ft= 5880lb-ft