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:
a) Em= K +U, b) Em= K
Explanation:
The system in this case is formed by the mobilizes and the hill.
Let's write the expressions correctly and completely.
a) When the car moves in the path, the mechanical energy is the siua of the kinetic energy of the car and the potential energy of the car when going up the hill.
Em = K + U
be) when the car moves in the flat part all the mechanical energy is formed by its kinetic energy that is calculated with the mass and speed of the car
Em = K
c) When the car goes up the hill the energy the mechanical energy is conserved, but part of the kinetic energy is transformed into potential energy.
Explanation:
Position-time graphs measure/express the position of a skater over time relative to the start or finish of the race (depends on how it is used). Note: are the skaters in line vertically or horizontally? Like is one directly behind the other or are they next to each other?
If the two skaters are in line horizontally with each other, then their position will be the same relative to the start or finish of the race. This means if one passes the other one, the position would be different for all times after they pass. On the graph, it would look like one single line at the start (as position is same) which splits into 2 (representing the new difference in position due to 1 passing the other.
If the two skaters are in line vertically, their lines on the graph will appear parallel to each other (assuming they are going same speed) because the position is changing at the same rate, one is just reaching the same point after the other. If the skater behind overtakes the one in front. The lines on the graph will cross and continue either in parallel but with the other line on top to represent the moment where their position is the same right before they pass and after, where the second skater is now in front.
Hope this helped!