1) Star from the definition of power:
P = work/ time = W / Δt
We know that work is given by force times displacement:
W = F · Δd
Substituting in our formula:
P = F · Δd / <span>Δt
But we know by definition that </span>Δd / <span>Δt = velocity, therefore we can write:
</span>P = F · v
which is the alternative formula saying that Power is equal to Force times Velocity
2) No, it is not a violation of the Law of conservation of energy because as the spring slows down, the kinetic energy is transformed into potential energy and their sum stays constant.
If we assume that there is no friction between the tire and the ground, we can the use formula:
ΔKE + ΔPE = 0
where KE is the kinetic energy which is equal to 0.5mv²
and PE is the potential energy which is equal to mgh
Substituting the given values:
0.5 (10.5) (v2 - 2.10^2) + 10.5 (9.81) (8.59 - 22.4) = 0
Solving for v:
v = 16.59 m/s
Answer:
The magnitude of the vector A is <u>51 m.</u>
Explanation:
Given:
The horizontal component of a vector A is given as:
![A_x=44.4\ m](https://tex.z-dn.net/?f=A_x%3D44.4%5C%20m)
The vertical component of a vector A is given as:
![A_y=25.1\ m](https://tex.z-dn.net/?f=A_y%3D25.1%5C%20m)
Now, we know that, a vector A can be resolved into two mutually perpendicular components; one along the x axis and the other along the y axis. The magnitude of the vector A can be written as the square root of the sum of the squares of each component.
Therefore, the magnitude of vector A is given as:
![|\overrightarrow A|=\sqrt{A_{x}^2+A_{y}^2}](https://tex.z-dn.net/?f=%7C%5Coverrightarrow%20A%7C%3D%5Csqrt%7BA_%7Bx%7D%5E2%2BA_%7By%7D%5E2%7D)
Now, plug in 44.4 for
, 25.1 for
and solve for the magnitude of A. This gives,
![|\overrightarrow A|=\sqrt{(44.4)^2+(25.1)^2}\\|\overrightarrow A|=\sqrt{1971.36+630.01}\\|\overrightarrow A|=\sqrt{2601.37}\\|\overrightarrow A|=51\ m](https://tex.z-dn.net/?f=%7C%5Coverrightarrow%20A%7C%3D%5Csqrt%7B%2844.4%29%5E2%2B%2825.1%29%5E2%7D%5C%5C%7C%5Coverrightarrow%20A%7C%3D%5Csqrt%7B1971.36%2B630.01%7D%5C%5C%7C%5Coverrightarrow%20A%7C%3D%5Csqrt%7B2601.37%7D%5C%5C%7C%5Coverrightarrow%20A%7C%3D51%5C%20m)
Therefore, the magnitude of the vector A is 51 m.
Answer:
Depending on where people are located in the world (Northern hemisphere, Southern hemisphere, etc) depends on the difference in direction (North, South, east, West) which is most likely why it'd look different.
Explanation:
I dunno if this is along the lines of an answer you're looking for, but hope this helps :)