A spherical snowball melts at a rate proportional to its surface area. (a) write a differential equation for its volume, v. (use
1 answer:
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First we need to find the acceleration of the skier on the rough patch of snow.
We are only concerned with the horizontal direction, since the skier is moving in this direction, so we can neglect forces that do not act in this direction. So we have only one horizontal force acting on the skier: the frictional force,
. For Newton's second law, the resultant of the forces acting on the skier must be equal to ma (mass per acceleration), so we can write:
Where the negative sign is due to the fact the friction is directed against the motion of the skier.
Simplifying and solving, we find the value of the acceleration:
Now we can use the following relationship to find the distance covered by the skier before stopping, S:
where
is the final speed of the skier and 
is the initial speed. Substituting numbers, we find:
We are only concerned with the horizontal direction, since the skier is moving in this direction, so we can neglect forces that do not act in this direction. So we have only one horizontal force acting on the skier: the frictional force,
Where the negative sign is due to the fact the friction is directed against the motion of the skier.
Simplifying and solving, we find the value of the acceleration:
Now we can use the following relationship to find the distance covered by the skier before stopping, S:
where
Answer:
The change in potential energy and kinetic energy are 980 MJ and 148.3 MJ.
Explanation:
Given that,
Mass of aircraft = 10000 kg
Speed = 620 km/h = 172.22 m/s
Altitude = 10 km = 1000 m
We calculate the change in potential energy
For g = 10 m/s²,
The change in potential energy will be 1000 MJ.
We calculate the change in kinetic energy
For g = 10 m/s²,
The change in kinetic energy will be 150 MJ.
Hence, The change in potential energy and kinetic energy are 980 MJ and 148.3 MJ.