<span>Answer:
So this involves right triangles. The height is always 100. Let the horizontal be x and the length of string be z.
So we have x2 + 1002 = z2. Now take its derivative in terms of time to get
2x(dx/dt) = 2z(dz/dt)
So at your specific moment z = 200, x = 100âš3 and dx/dt = +8
substituting, that makes dz/dt = 800âš3 / 200 or 4âš3.
Part 2
sin a = 100/z = 100 z-1 . Now take the derivative in terms of t to get
cos a (da./dt) = -100/ z2 (dz/dt)
So we know z = 200, which makes this a 30-60-90 triangle, therefore a=30 degrees or π/6 radians.
Substitute to get
cos (Ď€/6)(da/dt) = (-100/ 40000)(4âš3)
âš3 / 2 (da/dt) = -âš3 / 100
da/dt = -1/50 radians</span>
<span>
The purpose of a gasoline car engine is to convert gasoline into motion
so that your car can move. Currently the easiest way to create motion
from gasoline is to burn the gasoline inside an engine.
Therefore, a car engine is an internal combustion engine -- combustion takes place internally.
There is such a thing as an external combustion engine. A steam engine
in old-fashioned trains and steam boats is the best example of an
external combustion engine. The fuel (coal, wood, oil, whatever) in a
steam engine burns outside the engine to create steam, and the steam
creates motion inside the engine. Internal combustion is a lot more
efficient (takes less fuel per mile) than external combustion, plus an
internal combustion engine is a lot smaller than an equivalent external
combustion engine. This explains why we don't see any cars using steam
engines.
To understand the basic idea behind how a reciprocating internal
combustion engine works, it is helpful to have a good mental image of
how "internal combustion" works.
One good example is an old Revolutionary War cannon. You have probably
seen these in movies, where the soldiers load the cannon with gun powder
and a cannon ball and light it. That is internal combustion, but it is
hard to imagine that having anything to do with engines.
A potato cannon uses the basic principle behind any reciprocating
internal combustion engine: If you put a tiny amount of high-energy fuel
(like gasoline) in a small, enclosed space and ignite it, an incredible
amount of energy is released in the form of expanding gas. You can use
that energy to propel a potato 500 feet. In this case, the energy is
translated into potato motion. You can also use it for more interesting
purposes. For example, if you can create a cycle that allows you to set
off explosions like this hundreds of times per minute, and if you can
harness that energy in a useful way, what you have is the core of a car
engine! </span>
Answer:
C
Explanation:
Magnitude of any quantity is the measurable value of the quantity. While the direction of the given quantity is the specific pointing direction of position or the angle at which it move.
The magnitude of the vector described below? 13 m/s to the east will be 13 m/s
While the direction will be eastward.
Therefore, the magnitude is 13 m/s
The correct answer is option C
Answer:
m³/(kg⋅s²)
Explanation:
Hello.
In this case, since the involved formula is:
By writing a dimensional analysis with the proper algebra handling, we obtain:
![N[=]G*\frac{kg*kg}{m^2}\\ \\kg*\frac{m}{s^2}[=]G *\frac{kg*kg}{m^2}\\\\G[=]\frac{kg*m*m^2}{kg^2*s^2}\\ \\G[=]\frac{m^3}{kg*s^2}](https://tex.z-dn.net/?f=N%5B%3D%5DG%2A%5Cfrac%7Bkg%2Akg%7D%7Bm%5E2%7D%5C%5C%20%5C%5Ckg%2A%5Cfrac%7Bm%7D%7Bs%5E2%7D%5B%3D%5DG%20%2A%5Cfrac%7Bkg%2Akg%7D%7Bm%5E2%7D%5C%5C%5C%5CG%5B%3D%5D%5Cfrac%7Bkg%2Am%2Am%5E2%7D%7Bkg%5E2%2As%5E2%7D%5C%5C%20%5C%5CG%5B%3D%5D%5Cfrac%7Bm%5E3%7D%7Bkg%2As%5E2%7D)
Thus, answer is:
m³/(kg⋅s²)
Note that the [=] is used to indicate the units of G.
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